Polar coding method and apparatus

ABSTRACT

Example polar coding methods and apparatus are described. One example method includes determining a sequence used to code to-be-coded bits. Polar coding is performed on the to-be-coded bits by using the sequence to obtain coded bits. The sequence is used to represent a reliability order of N polarized channels, N is a mother code length of a polar code, and N is a positive integer power of 2.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/236,002, filed on Dec. 28, 2018, which is a continuation ofInternational Application No. PCT/CN2018/092908, filed on Jun. 26, 2018,which claims priority to Chinese Patent Application No. 201710632016.8,filed on Jul. 28, 2017. All of the afore-mentioned patent applicationsare hereby incorporated by reference in their entireties.

TECHNICAL FIELD

Embodiments of this application relate to the field of communicationstechnologies, and in particular, to a polar coding method and apparatus.

BACKGROUND

As a most basic wireless access technology, channel coding plays acrucial role in ensuring reliable data transmission. In an existingwireless communications system, channel coding is usually performed byusing a turbo code, a low-density parity-check (LDPC) code, and a polarcode. The turbo code cannot support information transmission at anexcessively low or excessively high bit rate. However, for medium-packetor short-packet transmission, it is difficult for the turbo code and theLDPC code to implement desired performance when lengths of the codes arelimited, due to coding/decoding characteristics of the turbo code andthe LDPC code. In terms of implementation, the turbo code and the LDPCcode have relatively high calculation complexity in a coding/decodingimplementation process. Theoretically, it is proved that the polar codeis a good code that can achieve a Shannon capacity and has relativelysimple coding/decoding complexity, and for this reason, the polar codebecomes more widely applied.

However, with rapid evolution of the wireless communications system, afuture communications system, such as a fifth generation (5G)communications system, has some new characteristics. For example, threemost typical communications scenarios include an enhanced mobilebroadband (eMBB) Internet, massive machine type communication (mMTC),and ultra-reliable and low latency communications (URLLC). Thesecommunications scenarios impose a higher requirement on coding/decodingperformance of the polar code.

A reliability order of polarized channels plays an important role in thecoding/decoding performance of the polar code. However, in a currentphase, accuracy of the reliability order of the polarized channels isnot desired. Consequently, further improvement of the coding/decodingperformance of the polar code in an application process is affected.

SUMMARY

Embodiments of this application provide a polar coding method andapparatus, to improve accuracy of a reliability order of polarizedchannels.

According to a first aspect, a polar coding method is provided. At leasttwo sequences with relatively good performance are selected based on aperformance determining rule. Same sequence numbers at a same sortinglocation in the at least two sequences are determined. The determinedsame sequence numbers are determined as sequence numbers whosereliability remains unchanged in sequences, and the sequence numberswhose reliability remains unchanged in the sequences are sorted based onorders of the sequence numbers in the at least two sequences. Sequencenumbers in the at least two sequences other than the determined sequencenumbers whose reliability remains unchanged are compared to select somesubsequences, and locations of elements in the subsequences may bemutually exchanged. A sorting sequence obtained from above is used as asorting sequence used for polar coding in this embodiment of thisapplication. In this way, for the sorting sequence obtained by using theforegoing method, a plurality of sequences with relatively goodperformance can be comprehensively considered, and a sequence numberwhose reliability remains unchanged is determined by using anintersection set between different sequences. This helps improveaccuracy of a reliability order of polarized channels and improvecoding/decoding performance of a polar code.

In a possible design, a sequence used to code to-be-coded bits isdetermined, where the sequence is used to represent a reliability orderof N polarized channels; and polar coding is performed on theto-be-coded bits by using the sequence to obtain coded bits, where N isa mother code length of a polar code, and N is a positive integer powerof 2.

In a possible design, a length of the to-be-coded bits is K, the Kto-be-coded bits are mapped to K polarized channels in the N polarizedchannels, and reliability of the K polarized channels is higher thanreliability of remaining N−K polarized channels.

In a possible design, the sequence used to code the to-be-coded bits isdetermined based on the mother code length N and a preset sequence.

In a possible design, the sequence used to code the to-be-coded bits isall or a subset of another sequence, the another sequence includesN_(max) sequence numbers, the N_(max) sequence numbers are arranged inthe another sequence based on reliability of the N_(max) polarizedchannels, N_(max) is a positive integer power of 2, and N_(max)≥N.

In a possible design, the sequence meets a nesting characteristic, andthe nesting characteristic is as follows: A sequence with a relativelyshort mother code length of N₂ is obtained based on a sequence with arelatively long mother code length of N₁. Elements whose sequencenumbers are less than or equal to N₂ are extracted from the sequencewith the relatively long mother code length of N₁, and an obtainedsubsequence is the sequence with the relatively short mother code lengthof N₂. An order of the elements in the obtained sequence with therelatively short mother code length of N₂ is the same as an order ofthese elements in the sequence with the relatively long mother codelength of N₁.

In a possible design, N_(max) is a maximum mother code length of a polarcode, for example, N_(max)=1024, or N_(max)=512. The sequence needs tomeet the nesting characteristic. When a sequence with a maximum mothercode length is determined, another sequence with a relatively shortmother code length may be obtained based on the sequence with themaximum mother code length. For example, a sequence with a length of1024 and whose maximum mother code length is 1024 is determined.

Elements whose element values are less than or equal to 64 are extractedfrom the sequence with the length of 1024 to form a subsequence with alength of 64. An order of the elements in the obtained subsequence withthe length of 64 is the same as an order of these elements in thesequence with the length of 1024. That is, the extracted subsequencemeets the nesting characteristic. Similarly, sequences of lengths 128,256, and 512 may be extracted from the sequence with the length of 1024.The obtained sequences with the short mother code lengths are applied inthis embodiment of this application to code the to-be-coded bits.

In a possible design, the sequence may be a part or all of any one ofsequences (1) to (30) in the specification. When N=1024, the sequencemay be a part or all of any one of sequences S1 to S20 in thespecification.

In a possible design, when a value of N is 64, 128, 256, or 512, thesequence may be extracted from a preset sequence with a maximum mothercode length based on the nesting characteristic, or a sequencecorresponding to a code length in the sequences (1) to (30) in thespecification may be directly used.

Polar construction is performed by using the sequence, so as to helpimprove accuracy of evaluating reliability of a polarized channel,thereby improving coding/decoding performance of a polar code.

A minimum value of a sequence number in any one of the sequences S1 toS20 in the specification is 1, and sequence numbers are arranged inascending order of reliability of the N polarized channels. In apossible design, if the sequence numbers in the sequence are arranged inascending order of the reliability of the N polarized channels and aminimum value of the sequence numbers of the sequence is 0, a newsequence is obtained by sequentially subtracting 1 from the sequencenumbers in any sequence, and sequence performance is not affected.

Similarly, in a possible design, if the sequence numbers in the sequenceare arranged in descending order of the reliability of the N polarizedchannels, a new sequence may be obtained by arranging sequence numbersin any one of sequences S1 to S20 in the specification in a reverseorder, and the sequence performance is also not affected.

In a possible design, the sequence may also be represented by using asequence of normalized reliability or equivalent reliability ofchannels. For example, if a sorting location of a channel x in thesequence is n (a minimum sequence number in the sequence is denoted as1), reliability of the channel may be represented by n or normalizedn/N.

In a possible design, locations of a few elements in any one of thesequences S1 to S20 in the specification may be mutually exchanged. Forexample, a location of a sequence number may be adjusted within aspecified amplitude. For example, the specified amplitude is 5, and alocation of an element whose sequence number is 10 may be adjustedwithin a range from five locations on the left of the element to fivelocations on the right of the element.

According to a second aspect, a polar coding apparatus is provided, andthe apparatus has functions of implementing the method according to anyone of the first aspect or the possible designs of the first aspect. Thefunctions may be implemented by using hardware, or may be implemented byhardware executing corresponding software. The hardware or the softwareincludes one or more modules corresponding to the functions.

In a possible design, when some or all of the functions are implementedby using hardware, the polar coding apparatus includes: an inputinterface circuit, configured to obtain to-be-coded bits; a logiccircuit, configured to perform behaviors described in any one of thefirst aspect or the possible designs of the first aspect; and an outputinterface circuit, configured to output a coded bit sequence.

Optionally, the polar coding apparatus may be a chip or an integratedcircuit.

In a possible design, when some or all of the functions are implementedby using software, the polar coding apparatus includes: a memory,configured to store a program; and a processor, configured to executethe program stored in the memory. When the program is executed, thepolar coding apparatus may implement the method according to any one ofthe first aspect or the possible designs of the first aspect.

Optionally, the memory may be a physically independent unit, or may beintegrated into the processor.

In a possible design, when some or all of the functions are implementedby using software, the polar coding apparatus includes a processor. Amemory configured to store a program is located outside the codingapparatus. The processor is connected to the memory by using acircuit/wire, and is configured to read and execute the program storedin the memory.

According to a third aspect, a communications system is provided, wherethe communications system includes a transmit end and a receive end, andthe transmit end may perform the method according to the first aspect orany possible design of the first aspect.

According to a fourth aspect, a computer storage medium is provided,where the computer storage medium stores a computer program, and thecomputer program includes an instruction used to perform the methodaccording to any one of the first aspect or the possible designs of thefirst aspect.

According to a fifth aspect, an embodiment of this application providesa computer program product including an instruction. When theinstruction runs on a computer, the computer performs the method in theforegoing aspect.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic architectural diagram of a communications systemapplied to an embodiment of this application;

FIG. 2 is a schematic flowchart of a polar coding method according to anembodiment of this application;

FIG. 3 is a first schematic structural diagram of a polar codingapparatus according to an embodiment of this application;

FIG. 4 is a second schematic structural diagram of a polar codingapparatus according to an embodiment of this application;

FIG. 5 is a third schematic structural diagram of a polar codingapparatus according to an embodiment of this application; and

FIG. 6 is a fourth schematic structural diagram of a polar codingapparatus according to an embodiment of this application.

DESCRIPTION OF EMBODIMENTS

The following describes in detail the embodiments of this applicationwith reference to the accompanying drawings.

The embodiments of this application provide a polar coding method andapparatus. At least two sequences with relatively good performance areselected based on a performance determining rule. Same sequence numbersat a same sorting location in the at least two sequences are determined.The determined same sequence numbers are determined as sequence numberswhose reliability remains unchanged in sequences, and the sequencenumbers whose reliability remains unchanged in the sequences are sortedbased on orders of the sequence numbers in the at least two sequences.Sequence numbers in the at least two sequences other than the determinedsequence numbers whose reliability remains unchanged are compared toselect some subsequences, and locations of elements in the subsequencesmay be mutually exchanged. A sorting sequence obtained from above isused as a sorting sequence used for polar coding in the embodiments ofthis application. In this way, for the sorting sequence obtained byusing the foregoing method, a plurality of sequences with relativelygood performance can be comprehensively considered, and a sequencenumber whose reliability remains unchanged is determined by using anintersection set between different sequences. This helps improveaccuracy of a reliability order of polarized channels and improvecoding/decoding performance of a polar code.

To facilitate understanding of the embodiments of this application, apolar code is briefly described below.

A coding policy of the polar code is to transmit useful information of auser by using a noiseless channel, and transmit agreed information or noinformation at all on a noisy channel. The polar code is also a linearblock code, a coding matrix of the polar code is G_(N), a coding processis x₁ ^(N)=u₁ ^(N)G_(N), where u₁ ^(N)=(u₁, u₂, . . . , u_(N)) is abinary row vector, a length of u₁ ^(N) (namely, a code length) is N,G_(N) is an N×N matrix, and G_(N)=F₂ ^(⊗(log) ² ^((N))). F₂ ^(⊗(log) ²^((N))) is defined as a kronecker product of log₂ N matrices F₂. Thematrix

$F_{2} = {\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}.}$

In the coding process of the polar code, some bits in u₁ ^(N) are usedto carry information, and are referred to as an information bit set, anda set of indexes of the information bits is denoted as

. The other bits are set to fixed values on which a receive end and atransmit end pre-agreed, and are referred to as a fixed bit set or afrozen bit set (frozen bits), and a set of indexes of these bits isrepresented by a complementary set

^(c) of

. The coding process of the polar code is equivalent to x₁^(N)=u_(A)G_(N.)(A)⊕u_(A) _(c) G_(N.)(A^(C)), where G_(N)(A) is asub-matrix obtained by using rows corresponding to the indexes in theset

, and G_(N)(AC) is a sub-matrix obtained by using rows corresponding tothe indexes in the set

^(c). u

is a set of information bits in u₁ ^(N), and a quantity of theinformation bits is K. u_(A) _(c) is a set of fixed bits in u₁ ^(N), aquantity of the fixed bits is (N−K), and the fixed bits are known bits.These fixed bits are generally set to 0. However, the fixed bits may beset to any value provided that the receive end and the transmit endpre-agree on the value. Therefore, coding output of the polar code maybe simplified as x₁ ^(N)=u

G_(N)(

), where u

is the set of information bits in u₁ ^(N), u

is a row vector with a length of K, namely, |

|=K, |⋅| indicates a quantity of elements in the set, K is a size of aninformation block, G_(N)(

) is the sub-matrix that is in the matrix G_(N) and that is obtained byusing the rows corresponding to the indexes in the set

, and G_(N)(

) is a K×N matrix.

A construction process of the polar code is a selection process of theset

, and determines performance of the polar code. The construction processof the polar code generally includes: determining, based on a mothercode length N, that there are N polarized channels, where the Npolarized channels respectively correspond to N rows in the codingmatrix; and calculating reliability of the polarized channels, usingindexes of the first K polarized channels with relatively highreliability as elements in the set

, and using indexes corresponding to remaining (N−K) polarized channelsas elements in the set

^(c) of the indexes of the fixed bits. The set

determines locations of the information bits, and the set

^(c) determines locations of the fixed bits.

A sequence in the embodiments of this application is used to represent areliability order of the N polarized channels. N is a mother code lengthof the polar code, and N is a positive integer power of 2.

In a case, the sequence may include sequence numbers of the N polarizedchannels, and the sequence numbers of the N polarized channels arearranged in the sequence based on reliability of the N polarizedchannels, for example, may be arranged in descending order of thereliability, or may be arranged in ascending order of the reliability.For ease of description, such a sequence is referred to as a Q sequence.

In another case, the sequence may include values of the reliability ofthe N polarized channels. Optionally, the value of the reliability maybe a value of normalized reliability or a value of equivalentreliability. For example, if a sorting location of a channel x in thesequence is y and a minimum sequence number in the sequence is denotedas 1, reliability of the channel may be represented by y or normalizedy/N. Similarly, the values of the reliability of the N polarizedchannels may be arranged in the sequence in descending order of thereliability, or may be arranged in ascending order of the reliability.For ease of description, such a sequence is referred to as a Z sequence.

It can be learned that the Q sequence and the Z sequence may be mutuallyconverted. In other words, the Z sequence may be obtained if the Qsequence is known, and vice versa.

A value of an element in the sequence may range from 0 to N−1, or mayrange from 1 to N. In the embodiments of this application, an example inwhich the value of the element in the sequence ranges from 1 to N isused for description. It can be learned that another sequence whoseelements have a value ranging from 0 to N−1 may be obtained bysequentially subtracting 1 from values of elements in the sequence. Thetwo sequences have same performance, and each can represent thereliability order of the N polarized channels. In the embodiments ofthis application, an example in which the elements in the sequence arearranged in ascending order of the reliability is used for description.It may be understood that a sequence in which the elements are arrangedin descending order of the reliability may be obtained by arranging theelements in the sequence in a reverse order. The two sequences have sameperformance, and each can represent the reliability order of the Npolarized channels.

As shown in FIG. 1, a communications system 100 applied to an embodimentof this application includes a transmit end 101 and a receive end 102.The transmit end 101 may alternatively be referred to as a coding end,and the receive end 102 may alternatively be referred to as a decodingend. The transmit end 101 may be a base station, and the receive end 102is a terminal; or the transmit end 101 is a terminal, and the receiveend 102 is a base station. The base station is an apparatus that isdeployed in a radio access network and that is configured to provide awireless communication function for the terminal. The base station mayinclude various forms of a macro base station, a micro base station, arelay station, or an access point, or the like. The base station may beapplied to systems with different wireless access technologies, such asa Long Term Evolution (LTE) system, or more possible communicationssystems such as a fifth generation (5G) communications system. The basestation may further be another network device that has a function of abase station, and specially, may further be a terminal that serves as abase station in D2D communication. The terminal may include varioushandheld devices, in-vehicle devices, wearable devices, or computingdevices that have a wireless communication function, or anotherprocessing device connected to a wireless modem, various forms of userequipment (UE) or a mobile station (MS), or the like.

Based on a communications system architecture shown in FIG. 1, in theembodiments of this application, a polar coding method may be performedby the transmit end 101. The polar coding method provided in theembodiments of this application is described below in detail.

Based on the communications system architecture shown in FIG. 1, asshown in FIG. 2, a specific procedure of a polar coding method providedin an embodiment of this application is as follows.

Step 201: Determine a sequence used to code to-be-coded bits.

The sequence is used to represent a reliability order of N polarizedchannels, N is a mother code length of a polar code, and N is a positiveinteger power of 2.

Step 202: Perform polar coding on the to-be-coded bits by using thesequence to obtain coded bits.

If a length of the to-be-coded bits is K, the K to-be-coded bits aremapped to K polarized channels in the N polarized channels, andreliability of the K polarized channels is higher than reliability ofremaining N−K polarized channels.

Specifically, sequence numbers of the K polarized channels are selectedin descending order of reliability based on the determined sequence usedto code the to-be-coded bits, and the K to-be-coded bits are placed inthe selected K polarized channels.

In actual application, the sequence used to code the to-be-coded bitsmay be stored in an offline manner. After a transmission parameter (forexample, a code length and a bit rate) is given, an information bit setand a frozen bit set that are used to construct the polar code aredetermined by using the pre-stored sequence. For a specific determiningmethod, refer to the foregoing description of the polar coding process,and details are not described herein again. In addition, in thisembodiment of this application, if the sequence used to code theto-be-coded bits is a sequence with a relatively short code length, thesequence with the relatively short code length may be extracted from astored sequence with a relatively long mother code length based on anesting characteristic of the sequence.

Examples of Q sequences and Z sequences with various mother code lengthsare provided below, and the provided Q sequences and Z sequences bothmay be used to code the to-be-coded bits. In the following example,elements in the sequence are arranged in ascending order of reliabilityof the N polarized channels. L_(n) ^((m)) represents a subsequence inthe sequence, n is a sequence number of the subsequence in the sequence,1≤n≤N, n is a positive integer, m represents a length of an n^(th)subsequence in the sequence, locations of elements in the subsequenceL_(n) ^((m)) are changeable, and sequence numbers at locations outsidethe subsequence in the sequence are fixed. When the locations of theelements in the subsequence L_(n) ^((m)) are exchanged in L_(n) ^((m)),a sequence obtained after the exchange may be obtained based onsequences provided below.

Example 1

(1) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 11 subsequences whose element locations are changeable. A valueof n ranges from 1 to 11, and the sequence may be:

[1, 2, L₁ ^((m=3)), 17, 33, L₂ ^((m=9)), 21, 35, 25, L₃ ^((m=2)), L₄^((m=2)), L₅ ^((m=3)), 15, 22, L₆ ^((m=6)), 42, 29, L₇ ^((m=2)), 45, L₈^((m=2)), L₉ ^((m=2)), L₁₀ ^((m=2)), 40, 30, L₁₁ ^((m=2)), 46, 52, 47,54, 55, 58, 59, 61, 32, 48, 56, 60, 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=9))=(7, 4, 13, 6, 19, 10, 34, 18, 11); L₃ ^((m=2))=(8,37); L₄ ^((m=2))=(12, 41); L₅ ^((m=3))=(20, 14, 49); L₆ ^((m=6))=(27,36, 39, 23, 38, 26); L₇ ^((m=2))=(50, 43); L₈ ^((m=2))=(16, 51); L₉^((m=2))=(24, 53); L₁₀ ^((m=2))=(57, 28); and L₁₁ ^((m=2))=(44, 31).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (8, 37), (12, 41),(20, 14, 49), 15, 22, (27, 36, 39, 23, 38, 26), 42, 29, (50, 43), 45,(16, 51), (24, 53), (57, 28), 40, 30, (44, 31), 46, 52, 47, 54, 55, 58,59, 61, 32, 48, 56, 60, 62, 63, 64].

(2) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude two subsequences whose element locations are changeable. A valueof n is 1 or 2. The sequence may be [1, 2, L₂ ^((m=7)), L₂ ^((m=48)),55, 56, 61, 57, 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=7))=(5,9, 3, 11, 8, 20, 4); and L₂ ^((m=48))=(13, 16, 22, 10, 25, 27, 40, 6,15, 12, 24, 17, 28, 32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18,30, 21, 33, 31, 46, 23, 35, 38, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43,53, 54, 60, 44).

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4), (13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28, 32, 42, 19,34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 35, 38,48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44), 55, 56, 61, 57,62, 63, 64].

(3) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 23 subsequences whose element locations are changeable. A valueof n ranges from 1 to 23. The sequence may be: [1, 2, L₁ ^((m=3)), 17;33, L₂ ^((m=10)), 21, 35, 25, L₃ ^((m=4)), L₄ ^((m=2)), L₅ ^((m=4)), L₆^((m=2)), 22, L₇ ^((m=8)), 68, 42, 29, 70, L₈ ^((m=11)), 77, L₉^((m=5)), L₁₀ ^((m=2)), L₁₁ ^((m=7)), 52, L₁₂ ^((m=3)), 54, 78, L₁₃^((m=4)), L₁₄ ^((m=3)), L₁₅ ^((m=3)), 90, L₁₆ ^((m=3)), 103, 106, L₁₇^((m=2)), 107, L₁₈ ^((m=2)), L₁₉ ^((m=2)), L₂₀ ^((m=2)), L₂₁ ^((m=2)),L₂₂ ^((m=4)), 94, 108, 95, 110, 116, 111, 118, 119, 122, L₂₃ ^((m=2)),125, 96, 112, 120, 124, 126, 127, 128].

In a possible example, L_(n) ^((m)) a may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=10))=(7, 65, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=4))=(66, 8, 37, 67); L₄ ^((m=2))=(12, 41); L₅ ^((m=4))=(20, 14, 69,49); L₆ ^((m=2)) (15, 73); L₇ ^((m=8)) (27, 36, 81, 39, 23, 38, 26, 97);L₈ ^((m=11))=(50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53); L₉^((m=5))=(83, 57, 28, 98, 40); L₈ ^((m=21))=(85, 30); L₁ ^((m=21))=(44,99, 31, 89, 72, 46, 101); L₂ ^((m=21))=(47, 76, 105); L₃ ^((m=21))=(55,84, 58, 113); L₄ ^((m=21))=(86, 79, 59); L₅ ^((m=21))=(100, 87, 61); L₁₆^((m=3))=(102, 91, 32); L₁₇ ^((m=2))=(48, 93); L₁₈ ^((m=2))=(56, 114);L₁₉ ^((m=2))=(80, 109); L₂₀ ^((m=2))=(60, 115); L₂₁ ^((m=3))=(88, 62,117); L₂₂ ^((m=4))=(92, 63, 121, 104); and L₂₃ ^((m=2))=(123, 64).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37, 67),(12, 41), (20, 14, 69, 49), (15, 73), 22, (27, 36, 81, 39, 23, 38, 26,97), 68, 42, 29, 70, (50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77,(83, 57, 28, 98, 40), (85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47,76, 105), 54, 78, (55, 84, 58, 113), (86, 79, 59), (100, 87, 61), 90,(102, 91, 32), 103, 106, (48, 93), 107, (56, 114), (80, 109), (60, 115),(88, 62, 117), (92, 63, 121, 104), 94, 108, 95, 110, 116, 111, 118, 119,122, (123, 64), 125, 96, 112, 120, 124, 126, 127, 128].

(4) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one subsequence whose element locations are changeable. A valueof n is 1. The sequence may be: [1, 2, L₁ ^((m=121)), 125, 121, 126,127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=121))=(5,10, 3, 12, 8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33,38, 55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62,26, 43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80,84, 101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47,74, 57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106,95, 110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111,100, 113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118,119).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119), 125, 121,126, 127, 128].

(5) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude 25 subsequences whose element locations are changeable. A valueof n ranges from 1 to 25. The sequence may be: [1, 2, L₁ ^((m=3)), 17,33, L₂ ^((m=11)), 21, 35, 25, L₃ ^((m=28)), 29, L₄ ^((m=18)), L₅^((m=6)), L₆ ^((m=4)), L₇ ^((m=10)), L₈ ^((m=2)), L₉ ^((m=56)), L₁₀^((m=6)), L₁₁ ^((m=9)), L₁₂ ^((m=6))L₁₂ ^((m=6)), L₁₃ ^((m=15)), L₁₄^((m=2)), L₁₅ ^((m=6)), L₁₆ ^((m=10)), L₁₇ ^((m=2)), 215, 189, L₁₈^((m=4)), 219, L₁₉ ^((m=5)), L₂₀ ^((m=4)), L₂₁ ^((m=5)), L₂₂ ^((m=2)),L₂₃ ^((m=4)) 222, 236, 223, L₂₄ ^((m=5)), L₂₅ ^((m=4)), 253, 224, 240,248, 252, 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=11))=(7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11); L₃^((m=28))=(66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22,131, 27, 36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145); L₄^((m=18))=(70, 50, 75, 161, 43, 193, 71, 45, 132, 82, 16, 51, 135, 74,24, 53, 134, 77); L₅ ^((m=6))=(83, 138, 57, 28, 98, 40); L₆^((m=4))=(139, 85, 30, 146); L₇ ^((m=10))=(44, 99, 141, 31, 89, 147, 72,162, 46, 101); L₈ ^((m=2))=(149, 52); L₉ ^((m=56))=(47, 76, 105, 165,194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195, 79, 59, 169, 100,140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91, 201, 32, 103, 106,150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114, 155, 80, 225, 167,109, 60, 115, 196, 170, 157); L₁₀ ^((m=6))=(88, 62, 117, 171, 198, 178);L₁₁ ^((m=9))=(92, 202, 199, 63, 144, 173, 121, 104, 179); L₁₀^((m=6))=(203, 94, 152, 210, 181, 108); L₁₃ ^((m=15))=(95, 205, 156,110, 211, 185, 116, 168, 158, 226, 111, 213, 118, 172, 227); L₁₄^((m=8))=(159, 217, 119, 174, 122, 200, 180, 229); L₁₅ ^((m=6))=(175,123, 64, 233, 204, 182); L₁₆ ^((m=10))=(125, 206, 241, 183, 212, 96,186, 207, 187, 214); L₁₇ ^((m=2))=(228, 112); L₁₈ ^((m=4))=(218, 160,120, 230); L₁₉ ^((m=5))=(231, 176, 124, 234, 221); L₂₀ ^((m=4))=(126,235, 184, 242); L₂₁ ^((m=5))=(188, 208, 237, 127, 243); L₂₂^((m=3))=(216, 245, 190); L₂₃ ^((m=4))=(220, 249, 191, 232); L₂₄^((m=5))=(238, 244, 239, 246, 128); and L₂₅ ^((m=4))=(247, 250, 251,192).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145), 29, (70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77), (83, 138, 57, 28, 98, 40),(139, 85, 30, 146), (44, 99, 141, 31, 89, 147, 72, 162, 46, 101), (149,52), (47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136,195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143,91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166,114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157), (88, 62, 117, 171,198, 178), (92, 202, 199, 63, 144, 173, 121, 104, 179), (203, 94, 152,210, 181, 108), (95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111,213, 118, 172, 227), (159, 217, 119, 174, 122, 200, 180, 229), (175,123, 64, 233, 204, 182), (125, 206, 241, 183, 212, 96, 186, 207, 187,214), (228, 112), 215, 189, (218, 160, 120, 230), 219, (231, 176, 124,234, 221), (126, 235, 184, 242), (188, 208, 237, 127, 243), (216, 245,190), (220, 249, 191, 232), 222, 236, 223, (238, 244, 239, 246, 128),(247, 250, 251, 192), 253, 224, 240, 248, 252, 254, 255, 256].

(6) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=249)), 253, 249, 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=249))=(5,10, 3, 12, 8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36,43, 65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74,28, 48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71,102, 108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35,64, 53, 92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83,116, 121, 153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160,93, 125, 133, 167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180,185, 213, 159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30,67, 63, 105, 41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89,126, 132, 164, 99, 131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130,94, 135, 140, 175, 109, 145, 150, 181, 158, 186, 191, 217, 114, 152,161, 189, 166, 196, 200, 223, 173, 203, 205, 225, 210, 232, 235, 248,56, 95, 106, 144, 112, 151, 155, 188, 122, 154, 162, 195, 169, 198, 204,226, 129, 165, 172, 201, 179, 206, 209, 230, 184, 211, 215, 233, 220,237, 239, 250, 139, 177, 182, 207, 190, 214, 216, 236, 194, 219, 222,238, 227, 240, 242, 251, 199, 224, 229, 241, 231, 243, 245, 252, 234,246, 247).

In this example, the Q sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247), 253, 249,254, 255, 256].

(7) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude 10 subsequences whose element locations are changeable. A valueof n ranges from 1 to 10. The sequence may be: [1, 2, L₁ ^((m=3)), 17,33, L₂ ^((m=11)), L₃ ^((m=4)), L₄ ^((m=419)), L₅ ^((m=6)), L₆ ^((m=29)),L₇ ^((m=23)), L₈ ^((m=5)), 507, L₉ ^((m=2)), L₁₀ ^((m=2)), 508, 510,511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=11))=(7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11); L₃^((m=4))=(257, 21, 35, 25); L₄ ^((m=419))=(66, 8, 37, 67, 130, 12, 41,20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23,261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 273, 193,71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321, 134, 77, 83, 138,57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44, 99, 141, 31, 89,263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267, 105, 274, 165,194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86, 136, 290, 195, 79,291, 59, 277, 169, 100, 140, 197, 87, 177, 61, 90, 281, 102, 148, 293,142, 322, 143, 91, 201, 32, 103, 264, 106, 323, 150, 297, 48, 93, 209,268, 386, 325, 305, 164, 154, 151, 107, 56, 166, 387, 329, 270, 114,155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170, 157, 88, 62, 278,292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294, 199, 63, 144, 337,173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298, 152, 210, 285,181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306, 301, 211, 185,327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172, 331, 227, 388,309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174, 122, 200, 180,229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449, 354, 395, 233,204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183, 402, 212, 397,345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214, 302, 228, 303,361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160, 120, 230, 334,409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335, 124, 234, 315,342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317, 343, 346, 404,288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127, 243, 406, 216,399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363, 465, 407, 422,249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336, 371, 222, 452,426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238, 348, 244, 455,319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350, 128, 408, 437,364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424, 467, 251, 372,192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430, 224, 456, 473,378, 436, 320, 485); L₅ ^((m=6))=(431, 489, 460, 240, 379, 438); L₆^((m=28))=(462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468, 368,443, 475, 484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487, 490,255, 477); L₇ ^((m=23))=(440, 493, 382, 499, 464, 491, 383, 472, 498,444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479, 384, 500);L₈ ^((m=5))=(503, 495, 502, 448, 506); L₉ ^((m=2))=(480, 509); and L₁₀^((m=2))=(504, 496).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), (257, 21, 35, 25), (66,8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27,36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50,75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53,321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146,44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76,267, 105, 274, 165, 194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113,86, 136, 290, 195, 79, 291, 59, 277, 169, 100, 140, 197, 87, 177, 61,90, 281, 102, 148, 293, 142, 322, 143, 91, 201, 32, 103, 264, 106, 323,150, 297, 48, 93, 209, 268, 386, 325, 305, 164, 154, 151, 107, 56, 166,387, 329, 270, 114, 155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170,157, 88, 62, 278, 292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294,199, 63, 144, 337, 173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298,152, 210, 285, 181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306,301, 211, 185, 327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172,331, 227, 388, 309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174,122, 200, 180, 229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449,354, 395, 233, 204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183,402, 212, 397, 345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214,302, 228, 303, 361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160,120, 230, 334, 409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335,124, 234, 315, 342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317,343, 346, 404, 288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127,243, 406, 216, 399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363,465, 407, 422, 249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336,371, 222, 452, 426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238,348, 244, 455, 319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350,128, 408, 437, 364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424,467, 251, 372, 192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430,224, 456, 473, 378, 436, 320, 485), (431, 489, 460, 240, 379, 438),(462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468, 368, 443, 475,484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487, 490, 255, 477),(440, 493, 382, 499, 464, 491, 383, 472, 498, 444, 501, 446, 447, 476,488, 478, 494, 505, 256, 492, 479, 384, 500), (503, 495, 502, 448, 506),507, (480, 509), (504, 496), 508, 510, 511, 512].

(8) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 374, 269,324, 332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413,450, 368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95,148, 52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184,186, 249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185,140, 195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224,233, 292, 242, 303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440,74, 142, 150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311,322, 378, 199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393,359, 406, 412, 452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349,364, 410, 376, 417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469,397, 438, 446, 463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251,259, 318, 209, 261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339,302, 352, 366, 408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300,293, 357, 314, 367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471,343, 391, 403, 439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487,488, 502, 266, 305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444,415, 448, 455, 480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470,461, 489, 475, 491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490,443, 473, 481, 495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501,499, 507, 493, 503, 504, 509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506), 510, 511, 512].

(9) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three subsequences whose element locations are changeable. Avalue of n ranges from 1 to 3. The sequence may be: [1, 2, L₁ ^((m=3)),17, 33, L₂ ^((m=1011)), L₂ ^((m=2)), 1020, 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1011))=(7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11,257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49,15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26,97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45,132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57,28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31,89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846,921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501, 446,933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908,488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700,494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384,911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875,977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993,448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966,939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872,971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,33, (7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559,786, 433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362,127, 243, 590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457,787, 349, 245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803,407, 681, 422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709,481, 614, 232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612,452, 602, 426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544,373, 655, 223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244,721, 455, 666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459,626, 400, 663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782,898, 408, 667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682,250, 627, 461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629,424, 901, 467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683,414, 604, 794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685,905, 253, 616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836,473, 810, 378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431,607, 717, 489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438,697, 462, 738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352,725, 784, 470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497,902, 821, 729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686,851, 484, 692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635,445, 694, 745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474,853, 637, 798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255,718, 608, 931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699,382, 814, 624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962,844, 491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498,881, 743, 444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733,447, 963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855,858, 916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874,639, 755, 256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702,932, 861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761,882, 495, 703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964,506, 938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860,756, 480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862,978, 876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887,936, 979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927,886, 995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997,891, 950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009,980, 880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986,944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003,895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012,768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021), (1016,1008), 1020, 1022, 1023, 1024].

(10) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1019)), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=1019))=0,11, 3, 13, 8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40,48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89,30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185,84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104,38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206,101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163,234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213,280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69,32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153,110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107,122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411,147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482,498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332,252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389,406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508,331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570,588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49,94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197,140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134,138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471,177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528,551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388,299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441,461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559,377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625,601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286,222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349,362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723,290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638,659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802,730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568,561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795,646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733,750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858,806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76,121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166,142, 237, 180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533,96, 161, 207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436,449, 541, 241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587,509, 614, 626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343,353, 456, 366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600,405, 521, 531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507,537, 634, 438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680,603, 691, 713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216,264, 342, 233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627,310, 402, 421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694,709, 780, 320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697,631, 715, 735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762,771, 835, 790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719,529, 622, 644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763,784, 853, 704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778,726, 792, 801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826,843, 898, 859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008,179, 253, 278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575,596, 689, 322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722,655, 746, 753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647,663, 749, 679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861,724, 805, 812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671,665, 767, 594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797,744, 818, 827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721,741, 819, 768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969,800, 870, 881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989,995, 1013, 375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821,756, 832, 850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873,862, 922, 888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926,816, 885, 892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955,964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883,830, 891, 900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912,927, 968, 935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015,877, 932, 941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003,1011, 1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012,1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898,859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253,278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689,322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746,753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749,679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861, 724, 805,812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 767,594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818,827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819,768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969, 800, 870,881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989, 995, 1013,375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821, 756, 832,850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873, 862, 922,888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926, 816, 885,892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955, 964, 987,924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891,900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912, 927, 968,935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932,941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003, 1011,1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016,1021, 1018), 1022, 1023, 1024].

Example 2

(11) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 12 subsequences whose element locations are changeable. A valueof n ranges from 1 to 12. The sequence may be: [1, 2, L₁ ^((m=3)), 17,L₂ ^((m=10)), 21, 35, 25, L₃ ^((m=2)), L₄ ^((m=2)), L₅ ^((m=3)), 15, 22,L₆ ^((m=6)), L₇ ^((m=2)), L₇ ^((m=5)), L₈ ^((m=2)), L₉ ^((m=2)), 40, 30,L₁₀ ^((m=2)), 46, 52, 47, 54, 55, 58, 59, L₁₂ ^((m=2)), 48, 56, 60, 62,63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=10))=(33, 7, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=2))=(8, 37); L₄ ^((m=2))=(12, 41); L₅ ^((m=3))=(20, 14, 49); L₆^((m=6))=(27, 36, 39, 23, 38, 26); L₇ ^((m=2))=(42, 29); L₈^((m=5))=(50, 43, 45, 16, 51); L₉ ^((m=2))=(24, 53); L₁₀ ^((m=2))=(57,28); L₁₁ ^((m=2))=(44, 31); and L₁₂ ^((m=2))=(61, 32).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (8, 37), (12, 41),(20, 14, 49), 15, 22, (27, 36, 39, 23, 38, 26), (42, 29), (50, 43, 45,16, 51), (24, 53), (57, 28), 40, 30, (44, 31), 46, 52, 47, 54, 55, 58,59, (61, 32), 48, 56, 60, 62, 63, 64].

(12) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=59))=(5,9, 3, 11, 8, 20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28,32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46,23, 35, 38, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55,56, 61, 57).

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28, 32, 42, 19,34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 35, 38,48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55, 56, 61, 57),62, 63, 64].

(13) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 23 (n=23) subsequences whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=3)), 17, L₂ ^((m=11)), 21, 35, 25,L₃ ^((m=4)), L₄ ^((m=2)), L₅ ^((m=4)), L₆ ^((m=2)), 22, L₇ ^((m=9)), L₈^((m=2)), L₉ ^((m=12)), 77, L₁₀ ^((m=5)), L₁₁ ^((m=2)), L₁₂ ^((m=7)),52, L₁₃ ^((m=2)), 54, L₁₄ ^((m=5)), L₁₅ ^((m=2)), L₁₆ ^((m=7)), 103, L₁₇^((m=3)), L₁₈ ^((m=3)), L₁₉ ^((m=2)), L₂₀ ^((m=2)), L₂₁ ^((m=3)), L₂₂^((m=4)), 94, 108, 95, 110, 116, 111, 118, 119, L₂₃ ^((m=5)), 112, 120,124, 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=11))=(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11); L₃^((m=4))=(66, 8, 37, 67); L₄ ^((m=2))=(12, 41); L₅ ^((m=4))=(20, 14, 69,49); L₆ ^((m=2))=(15, 73); L₇ ^((m=9))=(27, 36, 81, 39, 23, 38, 26, 97,68); L₈ ^((m=2))=(42, 29); L₉ ^((m=12))=(70, 50, 75, 43, 71, 45, 82, 16,51, 74, 24, 53); L₁₀ ^((m=5))=(83, 57, 28, 98, 40); L₁₁ ^((m=2))=(85,30); L₁₂ ^((m=7))=(44, 99, 31, 89, 72, 46, 101); L₁₃ ^((m=3))=(47, 76,105); L₁₄ ^((m=5))=(78, 55, 84, 58, 113); L₁₅ ^((m=3))=(86, 79, 59); L₁₆^((m=7))=(100, 87, 61, 90, 102, 91, 32); L₁₇ ^((m=3))=(106, 48, 93); L₁₈^((m=3))=(107, 56, 114); L₁₉ ^((m=2))=(80, 109); L₂₀ ^((m=2))=(60, 115);L₂₁ ^((m=3))=(88, 62, 117); L₂₂ ^((m=4))=(92, 63, 121, 104); and L₂₃^((m=5))=(122, 123, 64, 125, 96).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37, 67),(12, 41), (20, 14, 69, 49), (15, 73), 22, (27, 36, 81, 39, 23, 38, 26,97, 68), (42, 29), (70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77,(83, 57, 28, 98, 40), (85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47,76, 105), 54, (78, 55, 84, 58, 113), (86, 79, 59), (100, 87, 61, 90,102, 91, 32), 103, (106, 48, 93), (107, 56, 114), (80, 109), (60, 115),(88, 62, 117), (92, 63, 121, 104), 94, 108, 95, 110, 116, 111, 118, 119,(122, 123, 64, 125, 96), 112, 120, 124, 126, 127, 128].

(14) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=123)), 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=123))=(5,10, 3, 12, 8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33,38, 55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62,26, 43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80,84, 101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47,74, 57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106,95, 110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111,100, 113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119,125, 121).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119, 125, 121),126, 127, 128].

(15) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude 16 subsequences whose element locations are changeable. A valueof n ranges from 1 to 16. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=12)), 21, 35, 25, L₃ ^((m=29)), L₄^((m=28)), L₅ ^((m=12)), L₆ ^((m=62)), L₇ ^((m=54)), L₈ ^((m=9)), L₉^((m=5)), L₁₀ ^((m=4)), L₁₁ ^((m=5)), L₁₂ ^((m=3)), L₁₃ ^((m=4)), 222,236, 223, L₁₄ ^((m=5)), L₁₅ ^((m=4)), L₁₆ ^((m=2)), 240, 248, 252, 254,255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=12))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11); L₃^((m=29))=(66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22,131, 27, 36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145, 29); L₄^((m=28))=(70, 50, 75, 161, 43, 193, 71, 45, 132, 82, 16, 51, 135, 74,24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139, 85, 30, 146); L₅^((m=12))=(44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52); L₆^((m=62))=(47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86,136, 195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142,143, 91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56,166, 114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117,171, 198, 178); L₇ ^((m=54))=(92, 202, 199, 63, 144, 173, 121, 104, 179,203, 94, 152, 210, 181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158,226, 111, 213, 118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229,175, 123, 64, 233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187,214); L₈ ^((m=9))=(228, 112, 215, 189, 218, 160, 120, 230, 219); L₉^((m=5))=(231, 176, 124, 234, 221); L₁₀ ^((m=4))=(126, 235, 184, 242);L₁₁ ^((m=5))=(188, 208, 237, 127, 243); L₁₂ ^((m=3))=(216, 245, 190);L₁₃ ^((m=4))=(220, 249, 191, 232); L₁₄ ^((m=5))=(238, 244, 239, 246,128); L₁₅ ^((m=4))=(247, 250, 251, 192); and L₁₆ ^((m=2))=(253, 224).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11), 21, 35, 25, (66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145, 29), (70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139,85, 30, 146), (44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52),(47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195,79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91,201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114,155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117, 171, 198,178), (92, 202, 199, 63, 144, 173, 121, 104, 179, 203, 94, 152, 210,181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111, 213,118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229, 175, 123, 64,233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214), (228,112, 215, 189, 218, 160, 120, 230, 219), (231, 176, 124, 234, 221),(126, 235, 184, 242), (188, 208, 237, 127, 243), (216, 245, 190), (220,249, 191, 232), 222, 236, 223, (238, 244, 239, 246, 128), (247, 250,251, 192), (253, 224), 240, 248, 252, 254, 255, 256].

(16) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=251)), 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: [L₁^((m=251))=(5, 10, 3, 12, 8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17,13, 29, 19, 36, 43, 65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39,24, 44, 42, 74, 28, 48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96,100, 134, 71, 102, 108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51,57, 85, 35, 64, 53, 92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113,147, 83, 116, 121, 153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117,124, 160, 93, 125, 133, 167, 141, 171, 178, 208, 103, 136, 143, 174,149, 180, 185, 213, 159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37,59, 30, 67, 63, 105, 41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84,118, 89, 126, 132, 164, 99, 131, 137, 170, 146, 176, 183, 212, 54, 86,97, 130, 94, 135, 140, 175, 109, 145, 150, 181, 158, 186, 191, 217, 114,152, 161, 189, 166, 196, 200, 223, 173, 203, 205, 225, 210, 232, 235,248, 56, 95, 106, 144, 112, 151, 155, 188, 122, 154, 162, 195, 169, 198,204, 226, 129, 165, 172, 201, 179, 206, 209, 230, 184, 211, 215, 233,220, 237, 239, 250, 139, 177, 182, 207, 190, 214, 216, 236, 194, 219,222, 238, 227, 240, 242, 251, 199, 224, 229, 241, 231, 243, 245, 252,234, 246, 247, 253, 249)].

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247, 253, 249),254, 255, 256].

(17) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude six subsequences whose element locations are changeable. A valueof n ranges from 1 to 6. The sequence may be: [1, 2, L₁ ^((m=2)), 17, L₂^((m=441)), L₃ ^((m=29)), L₄ ^((m=29)), 507, L₅ ^((m=2)), L₆ ^((m=2)),508, 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=441))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257,21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73,258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265,42, 145, 29, 70, 50, 75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289,51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385,139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46,101, 149, 52, 47, 76, 267, 105, 274, 165, 194, 54, 163, 269, 78, 153,275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291, 59, 277, 169, 100,140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142, 322, 143, 91, 201,32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268, 386, 325, 305, 164,154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80, 225, 167, 276, 109,271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279, 117, 171, 198, 178,282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 283, 121, 104, 179, 295,203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95, 205, 299, 353, 326,156, 110, 401, 306, 301, 211, 185, 327, 116, 168, 158, 226, 307, 330,111, 213, 118, 172, 331, 227, 388, 309, 159, 417, 338, 217, 272, 119,280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175, 394, 284,123, 64, 341, 449, 354, 395, 233, 204, 296, 286, 182, 125, 206, 241,287, 300, 355, 183, 402, 212, 397, 345, 96, 186, 207, 328, 403, 187,357, 308, 419, 214, 302, 228, 303, 361, 112, 418, 215, 405, 310, 189,450, 332, 218, 160, 120, 230, 334, 409, 311, 421, 219, 369, 231, 392,176, 314, 340, 335, 124, 234, 315, 342, 451, 221, 425, 356, 126, 235,184, 396, 242, 317, 343, 346, 404, 288, 398, 453, 433, 188, 358, 208,237, 347, 362, 127, 243, 406, 216, 399, 304, 359, 420, 457, 349, 245,190, 220, 312, 363, 465, 407, 422, 249, 191, 370, 410, 411, 481, 232,316, 365, 423, 336, 371, 222, 452, 426, 413, 454, 318, 236, 344, 373,223, 427, 434, 238, 348, 244, 455, 319, 377, 429, 239, 360, 459, 400,435, 458, 246, 350, 128, 408, 437, 364, 466, 351, 247, 250, 461, 412,366, 441, 375, 424, 467, 251, 372, 192, 482, 414, 367, 469, 374, 428,415, 253, 483, 430, 224, 456, 473, 378, 436, 320, 485, 431, 489, 460,240, 379, 438); L₃ ^((m=28))=(462, 381, 248, 442, 352, 470, 439, 463,252, 497, 468, 368, 443, 475, 484, 380, 416, 254, 445, 486, 471, 376,474, 432, 487, 490, 255, 477); L₄ ^((m=28))=(440, 493, 382, 499, 464,491, 383, 472, 498, 444, 501, 446, 447, 476, 488, 478, 494, 505, 256,492, 479, 384, 500, 503, 495, 502, 448, 506); L₅ ^((m=2))=(480, 509);and L₆ ^((m=2))=(504, 496).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66, 8,37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 258, 22, 131, 27, 36,81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75,161, 43, 273, 193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321,134, 77, 83, 138, 57, 28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44,99, 141, 31, 89, 263, 147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267,105, 274, 165, 194, 54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86,136, 290, 195, 79, 291, 59, 277, 169, 100, 140, 197, 87, 177, 61, 90,281, 102, 148, 293, 142, 322, 143, 91, 201, 32, 103, 264, 106, 323, 150,297, 48, 93, 209, 268, 386, 325, 305, 164, 154, 151, 107, 56, 166, 387,329, 270, 114, 155, 80, 225, 167, 276, 109, 271, 60, 115, 196, 170, 157,88, 62, 278, 292, 279, 117, 171, 198, 178, 282, 92, 202, 389, 294, 199,63, 144, 337, 173, 283, 121, 104, 179, 295, 203, 94, 324, 393, 298, 152,210, 285, 181, 108, 95, 205, 299, 353, 326, 156, 110, 401, 306, 301,211, 185, 327, 116, 168, 158, 226, 307, 330, 111, 213, 118, 172, 331,227, 388, 309, 159, 417, 338, 217, 272, 119, 280, 333, 390, 174, 122,200, 180, 229, 339, 313, 391, 175, 394, 284, 123, 64, 341, 449, 354,395, 233, 204, 296, 286, 182, 125, 206, 241, 287, 300, 355, 183, 402,212, 397, 345, 96, 186, 207, 328, 403, 187, 357, 308, 419, 214, 302,228, 303, 361, 112, 418, 215, 405, 310, 189, 450, 332, 218, 160, 120,230, 334, 409, 311, 421, 219, 369, 231, 392, 176, 314, 340, 335, 124,234, 315, 342, 451, 221, 425, 356, 126, 235, 184, 396, 242, 317, 343,346, 404, 288, 398, 453, 433, 188, 358, 208, 237, 347, 362, 127, 243,406, 216, 399, 304, 359, 420, 457, 349, 245, 190, 220, 312, 363, 465,407, 422, 249, 191, 370, 410, 411, 481, 232, 316, 365, 423, 336, 371,222, 452, 426, 413, 454, 318, 236, 344, 373, 223, 427, 434, 238, 348,244, 455, 319, 377, 429, 239, 360, 459, 400, 435, 458, 246, 350, 128,408, 437, 364, 466, 351, 247, 250, 461, 412, 366, 441, 375, 424, 467,251, 372, 192, 482, 414, 367, 469, 374, 428, 415, 253, 483, 430, 224,456, 473, 378, 436, 320, 485, 431, 489, 460, 240, 379, 438), (462, 381,248, 442, 352, 470, 439, 463, 252, 497, 468, 368, 443, 475, 484, 380,416, 254, 445, 486, 471, 376, 474, 432, 487, 490, 255, 477), (440, 493,382, 499, 464, 491, 383, 472, 498, 444, 501, 446, 447, 476, 488, 478,494, 505, 256, 492, 479, 384, 500, 503, 495, 502, 448, 506), 507, (480,509), (504, 496), 508, 510, 511, 512].

(18) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 374, 269,324, 332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413,450, 368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95,148, 52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184,186, 249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185,140, 195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224,233, 292, 242, 303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440,74, 142, 150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311,322, 378, 199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393,359, 406, 412, 452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349,364, 410, 376, 417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469,397, 438, 446, 463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251,259, 318, 209, 261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339,302, 352, 366, 408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300,293, 357, 314, 367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471,343, 391, 403, 439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487,488, 502, 266, 305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444,415, 448, 455, 480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470,461, 489, 475, 491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490,443, 473, 481, 495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501,499, 507, 493, 503, 504, 509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506), 510, 511, 512].

(19) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three subsequences whose element locations are changeable. Avalue of n ranges from 1 to 3. The sequence may be: [1, 2, L₁ ^((m=2)),17, L₂ ^((m=1012)), L₃ ^((m=2)), 1020, 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1012))=(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18,11, 257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69,49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38,26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71,45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138,57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141,31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846,921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501, 446,933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908,488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700,494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384,911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875,977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993,448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966,939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872,971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559,786, 433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362,127, 243, 590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457,787, 349, 245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803,407, 681, 422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709,481, 614, 232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612,452, 602, 426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544,373, 655, 223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244,721, 455, 666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459,626, 400, 663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782,898, 408, 667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682,250, 627, 461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629,424, 901, 467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683,414, 604, 794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685,905, 253, 616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836,473, 810, 378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431,607, 717, 489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438,697, 462, 738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352,725, 784, 470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497,902, 821, 729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686,851, 484, 692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635,445, 694, 745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474,853, 637, 798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255,718, 608, 931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699,382, 814, 624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962,844, 491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498,881, 743, 444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733,447, 963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855,858, 916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874,639, 755, 256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702,932, 861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761,882, 495, 703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964,506, 938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860,756, 480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862,978, 876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887,936, 979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927,886, 995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997,891, 950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009,980, 880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986,944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003,895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012,768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021), (1016,1008), 1020, 1022, 1023, 1024].

(20) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1019)), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁^((m=1019))=(5, 11, 3, 13, 8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18,14, 31, 21, 40, 48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43,26, 51, 47, 89, 30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78,120, 127, 185, 84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35,59, 67, 104, 38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92,132, 146, 206, 101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143,109, 152, 163, 234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192,202, 269, 213, 280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574,15, 28, 41, 69, 32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57,95, 103, 153, 110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288,390, 62, 107, 122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230,301, 314, 411, 147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364,452, 386, 482, 498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160,221, 238, 332, 252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383,468, 293, 389, 406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307,396, 408, 508, 331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465,547, 480, 570, 588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39,45, 86, 49, 94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65,117, 126, 197, 140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345,445, 72, 134, 138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263,372, 374, 471, 177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420,510, 439, 528, 551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189,276, 283, 388, 299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440,532, 352, 441, 461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365,453, 473, 559, 377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516,611, 534, 625, 601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90,175, 187, 286, 222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469,563, 261, 349, 362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524,618, 630, 723, 290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538,628, 555, 638, 659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599,684, 711, 802, 730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549,643, 477, 568, 561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623,690, 737, 795, 646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635,717, 656, 733, 750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701,799, 776, 858, 806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975,993, 10, 33, 76, 121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249,257, 333, 87, 166, 142, 237, 180, 260, 292, 361, 178, 298, 268, 382,312, 399, 414, 533, 96, 161, 207, 275, 190, 295, 282, 393, 220, 308,321, 417, 335, 436, 449, 541, 241, 327, 344, 443, 355, 462, 470, 567,367, 481, 499, 587, 509, 614, 626, 738, 113, 188, 199, 302, 245, 315,334, 430, 229, 343, 353, 456, 366, 466, 483, 580, 271, 363, 376, 489,392, 472, 497, 600, 405, 521, 531, 619, 552, 649, 660, 759, 289, 391,401, 519, 422, 507, 537, 634, 438, 544, 571, 650, 582, 669, 685, 774,476, 562, 591, 680, 603, 691, 713, 788, 636, 706, 729, 810, 745, 820,842, 915, 148, 216, 264, 342, 233, 360, 369, 485, 285, 379, 394, 501,409, 525, 535, 627, 310, 402, 421, 511, 437, 554, 564, 652, 455, 550,578, 666, 602, 694, 709, 780, 320, 429, 448, 558, 459, 565, 586, 677,493, 589, 617, 697, 631, 715, 735, 804, 515, 615, 642, 718, 657, 731,748, 823, 674, 762, 771, 835, 790, 855, 872, 931, 325, 458, 487, 593,505, 612, 624, 719, 529, 622, 644, 739, 661, 758, 770, 833, 548, 653,672, 752, 688, 763, 784, 853, 704, 789, 798, 860, 813, 879, 889, 942,584, 676, 696, 778, 726, 792, 801, 868, 732, 811, 824, 886, 838, 895,904, 951, 751, 826, 843, 898, 859, 908, 916, 956, 869, 919, 928, 966,937, 976, 985, 1008, 179, 253, 278, 380, 318, 400, 418, 539, 305, 424,442, 556, 457, 575, 596, 689, 322, 450, 478, 573, 495, 598, 610, 710,517, 620, 639, 722, 655, 746, 753, 834, 329, 474, 491, 608, 523, 637,629, 734, 546, 647, 663, 749, 679, 773, 775, 851, 569, 668, 692, 766,703, 782, 796, 861, 724, 805, 812, 880, 825, 890, 901, 948, 354, 527,503, 645, 560, 671, 665, 767, 594, 683, 699, 786, 712, 793, 809, 876,607, 700, 716, 797, 744, 818, 827, 887, 755, 828, 840, 897, 857, 911,918, 962, 640, 721, 741, 819, 768, 846, 854, 905, 777, 841, 863, 913,874, 923, 934, 969, 800, 870, 881, 930, 893, 940, 925, 980, 902, 946,954, 973, 957, 989, 995, 1013, 375, 576, 543, 682, 605, 702, 707, 803,632, 728, 736, 821, 756, 832, 850, 907, 658, 742, 764, 829, 781, 852,865, 914, 794, 873, 862, 922, 888, 933, 939, 974, 686, 779, 760, 856,808, 867, 882, 926, 816, 885, 892, 943, 903, 936, 950, 982, 839, 896,909, 947, 917, 955, 964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017,725, 785, 815, 883, 830, 891, 900, 945, 845, 910, 906, 958, 921, 952,965, 992, 864, 912, 927, 968, 935, 963, 979, 996, 944, 981, 971, 999,986, 1004, 1006, 1015, 877, 932, 941, 972, 953, 978, 983, 1002, 959,984, 994, 1009, 988, 1003, 1011, 1020, 967, 997, 990, 1007, 1000, 1014,1010, 1019, 1005, 1012, 1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898,859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253,278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689,322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746,753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749,679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861, 724, 805,812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 767,594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818,827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819,768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969, 800, 870,881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989, 995, 1013,375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821, 756, 832,850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873, 862, 922,888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926, 816, 885,892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955, 964, 987,924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891,900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912, 927, 968,935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932,941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003, 1011,1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016,1021, 1018), 1022, 1023, 1024].

Example 3

(21) When N=64, the sequence is a Q sequence, and the Q sequence mayinclude 11 subsequences whose element locations are changeable. A valueof n ranges from 1 to 11. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=15)), L₃ ^((m=2)), L₄ ^((m=3)), 15, 22,L₅ ^((m=6)), L₆ ^((m=2)), L₇ ^((m=5)), L₈ ^((m=2)), L₉ ^((m=3)), 30, L₁₀^((m=2)), 46, 52, 47, 54, 55, 58, 59, L₁₁ ^((m=2))L, 48, 56, 60, 62, 63,64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=15))=(33, 7, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 8,37); L₃ ^((m=2))=(12, 41); L₄ ^((m=3))=(20, 14, 49); L₅ ^((m=6))=(27,36, 39, 23, 38, 26); L₆ ^((m=2))=(42, 29); L₇ ^((m=5))=(50, 43, 45, 16,51); L₈ ^((m=2))=(24, 53); L₉ ^((m=3))=(57, 28, 40); L₁₀ ^((m=2))=(44,31); and L₁₁ ^((m=2))=(61, 32).

N=64, and locations of elements in the subsequence L₁ ^((m=3)) in the Qsequence may be exchanged in the subsequence L₁ ^((m=3)), for example,may be (5, 9, 3), and may be exchanged to (3, 9, 5) or (5, 3, 9).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 8, 37), (12, 41), (20,14, 49), 15, 22, (27, 36, 39, 23, 38, 26), (42, 29), (50, 43, 45, 16,51), (24, 53), (57, 28, 40), 30, (44, 31), 46, 52, 47, 54, 55, 58, 59,(61, 32), 48, 56, 60, 62, 63, 64]. A set in parentheses is thesubsequence L_(n) ^((m)).

(22) When N=64, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=59)), 62, 63, 64].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=59))=(5,9, 3, 11, 8, 20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28,32, 42, 19, 34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46,23, 35, 38, 48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55,56, 61, 57). Locations of elements in L₁ ^((m=59)) may be exchanged inthe subsequence.

In this example, the Z sequence is specifically: [1, 2, (5, 9, 3, 11, 8,20, 4, 13, 16, 22, 10, 25, 27, 40, 6, 15, 12, 24, 17, 28, 32, 42, 19,34, 29, 45, 36, 47, 49, 58, 7, 14, 18, 30, 21, 33, 31, 46, 23, 35, 38,48, 39, 50, 52, 59, 26, 37, 41, 51, 43, 53, 54, 60, 44, 55, 56, 61, 57),62, 63, 64].

(23) When N=128, the sequence is a Q sequence, and the Q sequence mayinclude 17 subsequences whose element locations are changeable. A valueof n ranges from 1 to 17. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=20)), L₃ ^((m=6)), 22, L₄ ^((m=11)), L₅^((m=12)), 77, L₆ ^((m=7)), L₇ ^((m=7)), 52, L₈ ^((m=4)), L₉ ^((m=15)),L₁₀ ^((m=4)), L₁₁ ^((m=3)), L₁₂ ^((m=2)), L₁₃ ^((m=2)), L₁₄ ^((m=3)),L₁₅ ^((m=4)), 94, L₁₆ ^((m=2)), 110, 116, 111, 118, L₁₇ ^((m=6)), 112,120, 124, 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=20)), =(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35,25, 66, 8, 37, 67, 12, 41); L₃ ^((m=6))=(20, 14, 69, 49, 15, 73); L₄^((m=11))=(27, 36, 81, 39, 23, 38, 26, 97, 68, 42, 29); L₅^((m=12))=(70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53); L₆^((m=7))=(83, 57, 28, 98, 40, 85, 30); L₇ ^((m=7))=(44, 99, 31, 89, 72,46, 101); L₈ ^((m=4))=(47, 76, 105, 54); L₇ ^((m=15))=(78, 55, 84, 58,113, 86, 79, 59, 100, 87, 61, 90, 102, 91, 32); L₁₀ ^((m=4))=(103, 106,48, 93); L₁₁ ^((m=3))=(107, 56, 114); L₁₂ ^((m=2))=(80, 109); L₁₃^((m=2))=(60, 115); L₁₄ ^((m=3))=(88, 62, 117); L₁₅ ^((m=4))=(92, 63,121, 104); L₁₆ ^((m=2))=(108, 95); and L₁₇ ^((m=6))=(119, 122, 123, 64,125, 96).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 10, 34, 18, 11, 21, 35, 25, 66, 8, 37, 67, 12,41), (20, 14, 69, 49, 15, 73), 22, (27, 36, 81, 39, 23, 38, 26, 97, 68,42, 29), (70, 50, 75, 43, 71, 45, 82, 16, 51, 74, 24, 53), 77, (83, 57,28, 98, 40, 85, 30), (44, 99, 31, 89, 72, 46, 101), 52, (47, 76, 105,54), (78, 55, 84, 58, 113, 86, 79, 59, 100, 87, 61, 90, 102, 91, 32),(103, 106, 48, 93), (107, 56, 114), (80, 109), (60, 115), (88, 62, 117),(92, 63, 121, 104), 94, (108, 95), 110, 116, 111, 118, (119, 122, 123,64, 125, 96), 112, 120, 124, 126, 127, 128].

(34) When N=128, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=123)), 126, 127, 128].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=123))=(5,10, 3, 12, 8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33,38, 55, 20, 40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62,26, 43, 48, 65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80,84, 101, 87, 104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47,74, 57, 77, 83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106,95, 110, 112, 122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111,100, 113, 115, 123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119,125, 121).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 22, 4, 14, 17, 25, 11, 28, 31, 52, 6, 16, 13, 27, 18, 33, 38, 55, 20,40, 34, 60, 44, 64, 67, 91, 7, 15, 19, 35, 23, 39, 37, 62, 26, 43, 48,65, 50, 70, 73, 94, 30, 46, 53, 72, 56, 76, 78, 97, 59, 80, 84, 101, 87,104, 107, 120, 9, 21, 24, 42, 29, 45, 49, 69, 32, 54, 47, 74, 57, 77,83, 99, 36, 51, 58, 79, 63, 82, 86, 103, 68, 88, 90, 106, 95, 110, 112,122, 41, 61, 66, 85, 71, 89, 92, 109, 75, 93, 96, 111, 100, 113, 115,123, 81, 98, 102, 114, 105, 116, 117, 124, 108, 118, 119, 125, 121),126, 127, 128].

(25) When N=256, the sequence is a Q sequence, and the Q sequence mayinclude nine subsequences whose element locations are changeable. Avalue of n ranges from 1 to 9. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=9)), L₃ ^((m=14)), L₄ ^((m=3)), L₅^((m=4)), 222, L₆ ^((m=2)), L₇ ^((m=5)), L₈ ^((m=4)), L₉ ^((m=2)), 240,248, 252, 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=209))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 21,35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22,131, 27, 36, 81, 137, 39, 23, 38, 26, 97, 68, 42, 145, 29, 70, 50, 75,161, 43, 193, 71, 45, 132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83,138, 57, 28, 98, 40, 139, 85, 30, 146, 44, 99, 141, 31, 89, 147, 72,162, 46, 101, 149, 52, 47, 76, 105, 165, 194, 54, 163, 78, 153, 55, 84,58, 113, 86, 136, 195, 79, 59, 169, 100, 140, 197, 87, 177, 61, 90, 102,148, 142, 143, 91, 201, 32, 103, 106, 150, 48, 93, 209, 164, 154, 151,107, 56, 166, 114, 155, 80, 225, 167, 109, 60, 115, 196, 170, 157, 88,62, 117, 171, 198, 178, 92, 202, 199, 63, 144, 173, 121, 104, 179, 203,94, 152, 210, 181, 108, 95, 205, 156, 110, 211, 185, 116, 168, 158, 226,111, 213, 118, 172, 227, 159, 217, 119, 174, 122, 200, 180, 229, 175,123, 64, 233, 204, 182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214,228, 112, 215, 189, 218, 160, 120, 230, 219); L₃ ^((m=14))=(231, 176,124, 234, 221, 126, 235, 184, 242, 188, 208, 237, 127, 243); L₄^((m=3))=(216, 245, 190); L₅ ^((m=4))=(220, 249, 191, 232); L₆^((m=2))=(236, 223); L₇ ^((m=5))=(238, 244, 239, 246, 128); L₈^((m=4))=(247, 250, 251, 192); and L₉ ^((m=2))=(253, 224).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 21, 35, 25, 66, 8, 37,67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73, 22, 131, 27, 36, 81, 137,39, 23, 38, 26, 97, 68, 42, 145, 29, 70, 50, 75, 161, 43, 193, 71, 45,132, 82, 16, 51, 135, 74, 24, 53, 134, 77, 83, 138, 57, 28, 98, 40, 139,85, 30, 146, 44, 99, 141, 31, 89, 147, 72, 162, 46, 101, 149, 52, 47,76, 105, 165, 194, 54, 163, 78, 153, 55, 84, 58, 113, 86, 136, 195, 79,59, 169, 100, 140, 197, 87, 177, 61, 90, 102, 148, 142, 143, 91, 201,32, 103, 106, 150, 48, 93, 209, 164, 154, 151, 107, 56, 166, 114, 155,80, 225, 167, 109, 60, 115, 196, 170, 157, 88, 62, 117, 171, 198, 178,92, 202, 199, 63, 144, 173, 121, 104, 179, 203, 94, 152, 210, 181, 108,95, 205, 156, 110, 211, 185, 116, 168, 158, 226, 111, 213, 118, 172,227, 159, 217, 119, 174, 122, 200, 180, 229, 175, 123, 64, 233, 204,182, 125, 206, 241, 183, 212, 96, 186, 207, 187, 214, 228, 112, 215,189, 218, 160, 120, 230, 219), (231, 176, 124, 234, 221, 126, 235, 184,242, 188, 208, 237, 127, 243), (216, 245, 190), (220, 249, 191, 232),222, (236, 223), (238, 244, 239, 246, 128), (247, 250, 251, 192), (253,224), 240, 248, 252, 254, 255, 256].

(26) When N=256, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be:

[1, 2, L₁ ^((m=251)), 254, 255, 256].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=251))=(5,10, 3, 12, 8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36,43, 65, 21, 45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74,28, 48, 55, 79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71,102, 108, 142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35,64, 53, 92, 68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83,116, 121, 153, 128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160,93, 125, 133, 167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180,185, 213, 159, 187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30,67, 63, 105, 41, 70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89,126, 132, 164, 99, 131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130,94, 135, 140, 175, 109, 145, 150, 181, 158, 186, 191, 217, 114, 152,161, 189, 166, 196, 200, 223, 173, 203, 205, 225, 210, 232, 235, 248,56, 95, 106, 144, 112, 151, 155, 188, 122, 154, 162, 195, 169, 198, 204,226, 129, 165, 172, 201, 179, 206, 209, 230, 184, 211, 215, 233, 220,237, 239, 250, 139, 177, 182, 207, 190, 214, 216, 236, 194, 219, 222,238, 227, 240, 242, 251, 199, 224, 229, 241, 231, 243, 245, 252, 234,246, 247, 253, 249).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 23, 4, 15, 18, 27, 11, 31, 34, 61, 6, 17, 13, 29, 19, 36, 43, 65, 21,45, 38, 72, 50, 77, 82, 123, 7, 16, 20, 39, 24, 44, 42, 74, 28, 48, 55,79, 58, 87, 91, 127, 33, 52, 62, 90, 66, 96, 100, 134, 71, 102, 108,142, 115, 148, 156, 193, 9, 22, 25, 47, 32, 51, 57, 85, 35, 64, 53, 92,68, 98, 107, 138, 40, 60, 69, 101, 76, 104, 113, 147, 83, 116, 121, 153,128, 163, 168, 202, 46, 73, 80, 110, 88, 117, 124, 160, 93, 125, 133,167, 141, 171, 178, 208, 103, 136, 143, 174, 149, 180, 185, 213, 159,187, 192, 218, 197, 221, 228, 244, 14, 26, 37, 59, 30, 67, 63, 105, 41,70, 75, 111, 81, 119, 120, 157, 49, 78, 84, 118, 89, 126, 132, 164, 99,131, 137, 170, 146, 176, 183, 212, 54, 86, 97, 130, 94, 135, 140, 175,109, 145, 150, 181, 158, 186, 191, 217, 114, 152, 161, 189, 166, 196,200, 223, 173, 203, 205, 225, 210, 232, 235, 248, 56, 95, 106, 144, 112,151, 155, 188, 122, 154, 162, 195, 169, 198, 204, 226, 129, 165, 172,201, 179, 206, 209, 230, 184, 211, 215, 233, 220, 237, 239, 250, 139,177, 182, 207, 190, 214, 216, 236, 194, 219, 222, 238, 227, 240, 242,251, 199, 224, 229, 241, 231, 243, 245, 252, 234, 246, 247, 253, 249),254, 255, 256].

(27) When N=512, the sequence is a Q sequence, and the Q sequence mayinclude four subsequences whose element locations are changeable. Avalue of n ranges from 1 to 4. The sequence may be:

[1, 2, L₁ ^((m=3)), 17, L₂ ^((m=469)), L₃ ^((m=31)), L₄ ^((m=2)), 508,510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=469))=(33, 7, 65, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257,21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 14, 69, 49, 15, 73,258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 38, 26, 97, 68, 265,42, 145, 29, 70, 50, 75, 161, 43, 273, 193, 71, 45, 132, 82, 16, 289,51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 98, 40, 385,139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263, 147, 72, 266, 162, 46,101, 149, 52, 47, 76, 267, 105, 274, 165, 194, 54, 163, 269, 78, 153,275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291, 59, 277, 169, 100,140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142, 322, 143, 91, 201,32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268, 386, 325, 305, 164,154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80, 225, 167, 276, 109,271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279, 117, 171, 198, 178,282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 283, 121, 104, 179, 295,203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95, 205, 299, 353, 326,156, 110, 401, 306, 301, 211, 185, 327, 116, 168, 158, 226, 307, 330,111, 213, 118, 172, 331, 227, 388, 309, 159, 417, 338, 217, 272, 119,280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175, 394, 284,123, 64, 341, 449, 354, 395, 233, 204, 296, 286, 182, 125, 206, 241,287, 300, 355, 183, 402, 212, 397, 345, 96, 186, 207, 328, 403, 187,357, 308, 419, 214, 302, 228, 303, 361, 112, 418, 215, 405, 310, 189,450, 332, 218, 160, 120, 230, 334, 409, 311, 421, 219, 369, 231, 392,176, 314, 340, 335, 124, 234, 315, 342, 451, 221, 425, 356, 126, 235,184, 396, 242, 317, 343, 346, 404, 288, 398, 453, 433, 188, 358, 208,237, 347, 362, 127, 243, 406, 216, 399, 304, 359, 420, 457, 349, 245,190, 220, 312, 363, 465, 407, 422, 249, 191, 370, 410, 411, 481, 232,316, 365, 423, 336, 371, 222, 452, 426, 413, 454, 318, 236, 344, 373,223, 427, 434, 238, 348, 244, 455, 319, 377, 429, 239, 360, 459, 400,435, 458, 246, 350, 128, 408, 437, 364, 466, 351, 247, 250, 461, 412,366, 441, 375, 424, 467, 251, 372, 192, 482, 414, 367, 469, 374, 428,415, 253, 483, 430, 224, 456, 473, 378, 436, 320, 485, 431, 489, 460,240, 379, 438, 462, 381, 248, 442, 352, 470, 439, 463, 252, 497, 468,368, 443, 475, 484, 380, 416, 254, 445, 486, 471, 376, 474, 432, 487,490, 255, 477); L₃ ^((m=31))=(440, 493, 382, 499, 464, 491, 383, 472,498, 444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479, 384,500, 503, 495, 502, 448, 506, 507, 480, 509); and L₄ ^((m=2))=(504,496).

In this example, the Q sequence is specifically: [1, 43, 273, 193, 71,45, 132, 82, 16, 289, 51, 135, 74, 24, 53, 321, 134, 77, 83, 138, 57,28, 260, 98, 40, 385, 139, 85, 30, 262, 146, 44, 99, 141, 31, 89, 263,147, 72, 266, 162, 46, 101, 149, 52, 47, 76, 267, 105, 274, 165, 194,54, 163, 269, 78, 153, 275, 55, 84, 58, 113, 86, 136, 290, 195, 79, 291,59, 277, 169, 100, 140, 197, 87, 177, 61, 90, 281, 102, 148, 293, 142,322, 143, 91, 201, 32, 103, 264, 106, 323, 150, 297, 48, 93, 209, 268,386, 325, 305, 164, 154, 151, 107, 56, 166, 387, 329, 270, 114, 155, 80,225, 167, 276, 109, 271, 60, 115, 196, 170, 157, 88, 62, 278, 292, 279,117, 171, 198, 178, 282, 92, 202, 389, 294, 199, 63, 144, 337, 173, 283,121, 104, 179, 295, 203, 94, 324, 393, 298, 152, 210, 285, 181, 108, 95,205, 299, 353, 326, 156, 110, 401, 306, 301, 211, 185, 327, 116, 168,158, 226, 307, 330, 111, 213, 118, 172, 331, 227, 388, 309, 159, 417,338, 217, 272, 119, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313,391, 175, 394, 284, 123, 64, 341, 449, 354, 395, 233, 204, 296, 286,182, 125, 206, 241, 287, 300, 355, 183, 402, 212, 397, 345, 96, 186,207, 328, 403, 187, 357, 308, 419, 214, 302, 228, 303, 361, 112, 418,215, 405, 310, 189, 450, 332, 218, 160, 120, 230, 334, 409, 311, 421,219, 369, 231, 392, 176, 314, 340, 335, 124, 234, 315, 342, 451, 221,425, 356, 126, 235, 184, 396, 242, 317, 343, 346, 404, 288, 398, 453,433, 188, 358, 208, 237, 347, 362, 127, 243, 406, 216, 399, 304, 359,420, 457, 349, 245, 190, 220, 312, 363, 465, 407, 422, 249, 191, 370,410, 411, 481, 232, 316, 365, 423, 336, 371, 222, 452, 426, 413, 454,318, 236, 344, 373, 223, 427, 434, 238, 348, 244, 455, 319, 377, 429,239, 360, 459, 400, 435, 458, 246, 350, 128, 408, 437, 364, 466, 351,247, 250, 461, 412, 366, 441, 375, 424, 467, 251, 372, 192, 482, 414,367, 469, 374, 428, 415, 253, 483, 430, 224, 456, 473, 378, 436, 320,485, 431, 489, 460, 240, 379, 438, 462, 381, 248, 442, 352, 470, 439,463, 252, 497, 468, 368, 443, 475, 484, 380, 416, 254, 445, 486, 471,376, 474, 432, 487, 490, 255, 477), (440, 493, 382, 499, 464, 491, 383,472, 498, 444, 501, 446, 447, 476, 488, 478, 494, 505, 256, 492, 479,384, 500, 503, 495, 502, 448, 506, 507, 480, 509), (504, 496), 508, 510,511, 512].

(28) When N=512, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=507)), 510, 511, 512].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=507))=(5,10, 3, 12, 8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38,46, 72, 22, 49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83,29, 53, 60, 90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164,79, 119, 127, 177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97,36, 71, 58, 105, 76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182,94, 136, 144, 192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147,203, 107, 149, 163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187,237, 248, 309, 202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65,31, 75, 70, 122, 44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139,102, 151, 162, 211, 115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112,160, 109, 165, 173, 230, 129, 180, 188, 238, 200, 252, 260, 319, 134,190, 204, 255, 214, 273, 280, 333, 227, 286, 290, 344, 304, 361, 369,424, 62, 110, 124, 179, 132, 189, 196, 254, 145, 193, 206, 270, 217,275, 287, 346, 155, 212, 226, 282, 236, 294, 301, 353, 246, 307, 315,362, 328, 380, 389, 435, 172, 232, 240, 296, 256, 310, 317, 374, 269,324, 332, 386, 347, 392, 399, 445, 276, 335, 351, 394, 360, 405, 413,450, 368, 414, 422, 456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95,148, 52, 98, 106, 156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184,186, 249, 137, 191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185,140, 195, 205, 271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224,233, 292, 242, 303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440,74, 142, 150, 208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311,322, 378, 199, 245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393,359, 406, 412, 452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349,364, 410, 376, 417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469,397, 438, 446, 463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251,259, 318, 209, 261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339,302, 352, 366, 408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300,293, 357, 314, 367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471,343, 391, 403, 439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487,488, 502, 266, 305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444,415, 448, 455, 480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470,461, 489, 475, 491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490,443, 473, 481, 495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501,499, 507, 493, 503, 504, 509, 506).

In this example, the Z sequence is specifically: [1, 2, (5, 10, 3, 12,8, 24, 4, 15, 18, 28, 11, 32, 35, 67, 6, 17, 13, 30, 20, 38, 46, 72, 22,49, 40, 80, 55, 87, 93, 146, 7, 16, 21, 41, 25, 48, 45, 83, 29, 53, 60,90, 64, 100, 104, 153, 34, 57, 69, 103, 73, 111, 117, 164, 79, 119, 127,177, 135, 183, 197, 264, 9, 23, 26, 51, 33, 56, 63, 97, 36, 71, 58, 105,76, 114, 125, 171, 42, 66, 77, 118, 86, 121, 133, 182, 94, 136, 144,192, 154, 207, 216, 285, 50, 82, 91, 130, 101, 138, 147, 203, 107, 149,163, 215, 175, 222, 235, 299, 120, 169, 178, 229, 187, 237, 248, 309,202, 253, 263, 323, 274, 331, 350, 407, 14, 27, 39, 65, 31, 75, 70, 122,44, 78, 85, 131, 92, 141, 143, 198, 54, 89, 96, 139, 102, 151, 162, 211,115, 161, 170, 221, 181, 231, 243, 308, 59, 99, 112, 160, 109, 165, 173,230, 129, 180, 188, 238, 200, 252, 260, 319, 134, 190, 204, 255, 214,273, 280, 333, 227, 286, 290, 344, 304, 361, 369, 424, 62, 110, 124,179, 132, 189, 196, 254, 145, 193, 206, 270, 217, 275, 287, 346, 155,212, 226, 282, 236, 294, 301, 353, 246, 307, 315, 362, 328, 380, 389,435, 172, 232, 240, 296, 256, 310, 317, 374, 269, 324, 332, 386, 347,392, 399, 445, 276, 335, 351, 394, 360, 405, 413, 450, 368, 414, 422,456, 432, 465, 474, 494, 19, 37, 43, 81, 47, 88, 95, 148, 52, 98, 106,156, 113, 168, 176, 247, 61, 108, 116, 174, 128, 184, 186, 249, 137,191, 201, 262, 213, 272, 277, 340, 68, 123, 126, 185, 140, 195, 205,271, 152, 210, 218, 278, 225, 295, 297, 355, 159, 224, 233, 292, 242,303, 313, 363, 258, 320, 325, 375, 336, 385, 396, 440, 74, 142, 150,208, 158, 220, 228, 288, 167, 234, 239, 306, 250, 311, 322, 378, 199,245, 257, 321, 265, 326, 337, 387, 284, 338, 348, 393, 359, 406, 412,452, 219, 267, 279, 330, 291, 345, 356, 400, 298, 349, 364, 410, 376,417, 427, 459, 316, 370, 379, 423, 388, 429, 419, 469, 397, 438, 446,463, 449, 478, 482, 497, 84, 157, 166, 241, 194, 251, 259, 318, 209,261, 268, 334, 283, 341, 354, 402, 223, 281, 289, 339, 302, 352, 366,408, 312, 371, 372, 416, 383, 426, 431, 464, 244, 300, 293, 357, 314,367, 377, 420, 329, 382, 390, 430, 398, 434, 442, 471, 343, 391, 403,439, 409, 447, 454, 476, 418, 451, 460, 485, 466, 487, 488, 502, 266,305, 327, 381, 342, 384, 395, 436, 358, 404, 401, 444, 415, 448, 455,480, 365, 411, 421, 458, 428, 453, 468, 483, 437, 470, 461, 489, 475,491, 496, 505, 373, 425, 433, 462, 441, 467, 472, 490, 443, 473, 481,495, 477, 492, 500, 508, 457, 484, 479, 498, 486, 501, 499, 507, 493,503, 504, 509, 506), 510, 511, 512].

(29) When N=1024, the sequence is a Q sequence, and the Q sequence mayinclude three (n=3) subsequences whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=3)), 17, L₂ ^((m=1012)), L₃^((m=2)), 1020, 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁ ^((m=3))=(5,9, 3); L₂ ^((m=1012))=(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18,11, 257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69,49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261, 517, 38,26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273, 193, 71,45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77, 83, 138,57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44, 99, 141,31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577, 76, 267,105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525, 84, 58,113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100, 140, 197,87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143, 91, 201,546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209, 268, 386,325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387, 578, 329,549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115, 196, 170,157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178, 282, 92,553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121, 645,104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210, 285,181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534, 401,306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307, 548,330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159, 609,417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580, 122,200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394, 284,773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395, 233,204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563, 287,300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207, 328,646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302, 228,303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189, 450,332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774, 611,658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543, 335,124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356, 674,584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779, 564,404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588, 781,706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648,312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571,370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365, 423,336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454, 834,318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458, 817,246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621, 466,737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 374,575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430, 795,865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664, 722,320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668, 240,818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628, 248,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846,921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501, 446,933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638, 908,488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800, 700,494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479, 384,911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923, 875,977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848, 993,448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830, 966,939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751, 872,971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021); and L₃ ^((m=2))=(1016, 1008).

In this example, the Q sequence is specifically: [1, 2, (5, 9, 3), 17,(33, 7, 65, 513, 4, 13, 6, 19, 129, 10, 34, 18, 11, 257, 21, 35, 25, 66,8, 37, 67, 130, 12, 41, 20, 133, 514, 14, 69, 49, 15, 73, 258, 22, 131,27, 36, 81, 259, 137, 39, 23, 261, 517, 38, 26, 97, 68, 265, 42, 145,29, 70, 50, 75, 161, 43, 521, 273, 193, 71, 45, 132, 82, 16, 289, 51,135, 74, 515, 24, 53, 321, 134, 77, 83, 138, 57, 28, 260, 529, 98, 40,385, 139, 85, 30, 262, 146, 545, 44, 99, 141, 31, 89, 263, 147, 72, 519,266, 162, 46, 101, 149, 52, 47, 577, 76, 267, 105, 274, 165, 194, 54,516, 163, 269, 78, 153, 275, 55, 525, 84, 58, 113, 86, 136, 290, 518,195, 79, 291, 59, 277, 169, 531, 100, 140, 197, 87, 177, 641, 61, 90,281, 102, 148, 293, 522, 142, 322, 143, 91, 201, 546, 32, 103, 264, 106,530, 323, 150, 297, 48, 523, 93, 209, 268, 386, 325, 305, 537, 769, 533,164, 154, 151, 107, 56, 166, 387, 578, 329, 549, 270, 114, 155, 80, 225,167, 276, 109, 579, 271, 60, 115, 196, 170, 157, 88, 547, 62, 278, 292,520, 279, 117, 171, 198, 642, 178, 282, 92, 553, 202, 389, 294, 199,524, 63, 144, 337, 585, 173, 283, 121, 645, 104, 179, 295, 532, 203, 94,324, 561, 393, 298, 152, 581, 210, 285, 181, 526, 108, 95, 205, 770,299, 353, 326, 527, 156, 110, 534, 401, 306, 301, 643, 211, 185, 327,539, 116, 168, 593, 158, 226, 307, 548, 330, 111, 771, 213, 118, 172,551, 331, 227, 649, 388, 309, 159, 609, 417, 338, 535, 217, 272, 550,119, 280, 538, 333, 390, 174, 580, 122, 200, 777, 180, 229, 554, 339,657, 313, 541, 391, 175, 582, 394, 284, 773, 123, 673, 555, 785, 64,341, 705, 449, 562, 354, 801, 395, 233, 204, 528, 583, 557, 296, 286,182, 125, 206, 241, 644, 586, 563, 287, 300, 355, 183, 402, 212, 397,345, 587, 833, 565, 96, 186, 207, 328, 646, 536, 403, 594, 187, 357,589, 569, 308, 647, 419, 214, 302, 228, 303, 897, 595, 361, 112, 650,772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 160, 610, 597, 552,651, 120, 230, 334, 409, 542, 774, 611, 658, 311, 421, 601, 219, 369,231, 653, 392, 176, 314, 340, 543, 335, 124, 556, 775, 234, 315, 659,613, 342, 778, 451, 221, 425, 356, 674, 584, 126, 235, 184, 396, 242,558, 661, 617, 317, 343, 346, 779, 564, 404, 288, 398, 453, 675, 559,786, 433, 188, 358, 208, 665, 588, 781, 706, 677, 237, 347, 566, 362,127, 243, 590, 406, 216, 399, 567, 304, 598, 359, 802, 420, 625, 457,787, 349, 245, 570, 190, 591, 220, 648, 312, 707, 363, 596, 465, 803,407, 681, 422, 789, 249, 599, 191, 571, 370, 652, 410, 835, 411, 709,481, 614, 232, 573, 316, 660, 365, 423, 336, 689, 371, 793, 222, 612,452, 602, 426, 805, 413, 654, 454, 834, 318, 713, 236, 603, 344, 544,373, 655, 223, 615, 427, 776, 434, 560, 238, 899, 618, 348, 809, 244,721, 455, 666, 319, 605, 377, 662, 429, 780, 239, 676, 360, 837, 459,626, 400, 663, 678, 435, 568, 458, 817, 246, 619, 350, 788, 128, 782,898, 408, 667, 437, 592, 364, 621, 466, 737, 351, 679, 572, 247, 682,250, 627, 461, 708, 841, 412, 783, 366, 790, 441, 600, 375, 669, 629,424, 901, 467, 849, 804, 251, 791, 372, 710, 192, 574, 690, 482, 683,414, 604, 794, 367, 714, 469, 711, 374, 575, 656, 428, 807, 415, 685,905, 253, 616, 483, 633, 806, 430, 795, 865, 224, 691, 456, 715, 836,473, 810, 378, 606, 620, 436, 664, 722, 320, 797, 485, 693, 913, 431,607, 717, 489, 811, 460, 839, 668, 240, 818, 622, 379, 838, 723, 438,697, 462, 738, 680, 381, 813, 628, 248, 900, 842, 442, 623, 929, 352,725, 784, 470, 630, 819, 439, 670, 463, 739, 684, 252, 843, 850, 497,902, 821, 729, 468, 634, 903, 368, 671, 792, 443, 845, 631, 475, 686,851, 484, 692, 712, 380, 866, 796, 416, 825, 961, 741, 254, 906, 635,445, 694, 745, 486, 808, 687, 907, 471, 576, 716, 376, 867, 914, 474,853, 637, 798, 432, 695, 812, 487, 753, 724, 799, 490, 857, 909, 255,718, 608, 931, 477, 698, 726, 915, 440, 820, 840, 869, 493, 719, 699,382, 814, 624, 815, 499, 873, 740, 930, 672, 917, 822, 464, 727, 962,844, 491, 632, 730, 701, 383, 742, 846, 921, 472, 823, 852, 731, 498,881, 743, 444, 904, 688, 826, 501, 446, 933, 847, 636, 746, 827, 733,447, 963, 937, 476, 854, 868, 638, 908, 488, 696, 747, 829, 754, 855,858, 916, 965, 478, 910, 720, 800, 700, 494, 505, 749, 945, 859, 874,639, 755, 256, 969, 870, 492, 479, 384, 911, 816, 918, 728, 871, 702,932, 861, 500, 757, 732, 824, 923, 875, 977, 919, 503, 934, 744, 761,882, 495, 703, 922, 877, 502, 848, 993, 448, 734, 828, 883, 935, 964,506, 938, 748, 856, 925, 735, 830, 966, 939, 885, 507, 750, 946, 860,756, 480, 967, 831, 889, 941, 751, 872, 971, 912, 758, 947, 970, 862,978, 876, 920, 640, 759, 949, 863, 762, 509, 973, 924, 878, 953, 887,936, 979, 763, 504, 884, 704, 994, 926, 879, 981, 942, 765, 496, 927,886, 995, 736, 940, 985, 968, 890, 948, 832, 508, 943, 752, 974, 997,891, 950, 760, 893, 972, 1001, 954, 510, 864, 982, 951, 975, 764, 1009,980, 880, 955, 987, 996, 892, 928, 511, 766, 957, 998, 983, 888, 986,944, 999, 1002, 767, 989, 952, 1005, 894, 1011, 958, 976, 512, 1003,895, 984, 1010, 956, 988, 1013, 959, 1000, 1006, 990, 1017, 991, 1012,768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019, 960, 1021), (1016,1008), 1020, 1022, 1023, 1024].

(30) When N=1024, the sequence is a Z sequence, and the Z sequence mayinclude one (n=1) subsequence whose element locations are changeable.The sequence may be: [1, 2, L₁ ^((m=1019)), 1022, 1023, 1024].

In a possible example, L_(n) ^((m)) may be as follows: L₁^((m=1019))=(5, 11, 3, 13, 8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18,14, 31, 21, 40, 48, 77, 23, 52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43,26, 51, 47, 89, 30, 56, 63, 97, 68, 108, 112, 170, 36, 60, 73, 111, 78,120, 127, 185, 84, 130, 139, 201, 149, 208, 226, 323, 9, 24, 27, 54, 35,59, 67, 104, 38, 75, 61, 114, 81, 124, 137, 194, 44, 70, 82, 129, 92,132, 146, 206, 101, 150, 159, 219, 172, 239, 251, 356, 53, 88, 98, 143,109, 152, 163, 234, 116, 165, 184, 250, 198, 259, 277, 378, 131, 192,202, 269, 213, 280, 296, 395, 232, 303, 319, 416, 339, 431, 464, 574,15, 28, 41, 69, 32, 80, 74, 133, 46, 83, 91, 144, 99, 156, 158, 227, 57,95, 103, 153, 110, 168, 183, 244, 125, 182, 193, 258, 205, 272, 288,390, 62, 107, 122, 181, 118, 186, 196, 270, 141, 204, 214, 281, 230,301, 314, 411, 147, 217, 235, 306, 248, 338, 348, 433, 266, 357, 364,452, 386, 482, 498, 613, 66, 119, 136, 203, 145, 215, 224, 304, 160,221, 238, 332, 252, 340, 358, 454, 173, 246, 265, 350, 279, 371, 383,468, 293, 389, 406, 484, 426, 518, 536, 641, 195, 273, 284, 373, 307,396, 408, 508, 331, 419, 432, 530, 460, 542, 557, 667, 341, 435, 465,547, 480, 570, 588, 681, 496, 590, 609, 698, 633, 727, 757, 844, 20, 39,45, 86, 49, 94, 102, 164, 55, 106, 115, 174, 123, 191, 200, 294, 65,117, 126, 197, 140, 209, 212, 297, 151, 218, 231, 317, 247, 337, 345,445, 72, 134, 138, 210, 154, 223, 236, 336, 169, 243, 254, 346, 263,372, 374, 471, 177, 262, 274, 368, 287, 385, 403, 486, 311, 412, 420,510, 439, 528, 551, 654, 79, 157, 167, 240, 176, 256, 267, 359, 189,276, 283, 388, 299, 397, 415, 514, 228, 291, 309, 413, 324, 423, 440,532, 352, 441, 461, 545, 479, 572, 585, 687, 255, 328, 347, 428, 365,453, 473, 559, 377, 463, 488, 581, 512, 597, 621, 708, 407, 500, 516,611, 534, 625, 601, 740, 553, 648, 670, 720, 678, 772, 791, 849, 90,175, 187, 286, 222, 300, 313, 410, 242, 316, 330, 434, 351, 446, 469,563, 261, 349, 362, 444, 384, 467, 492, 577, 398, 502, 504, 595, 524,618, 630, 723, 290, 381, 370, 475, 404, 494, 513, 604, 427, 522, 538,628, 555, 638, 659, 747, 451, 540, 566, 651, 579, 673, 693, 765, 599,684, 711, 802, 730, 807, 814, 878, 326, 387, 425, 520, 447, 526, 549,643, 477, 568, 561, 664, 592, 675, 695, 783, 490, 583, 606, 705, 623,690, 737, 795, 646, 743, 714, 817, 761, 831, 848, 899, 506, 616, 635,717, 656, 733, 750, 822, 662, 754, 787, 847, 769, 836, 871, 938, 701,799, 776, 858, 806, 875, 866, 929, 837, 884, 894, 949, 920, 961, 975,993, 10, 33, 76, 121, 50, 135, 105, 211, 64, 155, 171, 225, 128, 249,257, 333, 87, 166, 142, 237, 180, 260, 292, 361, 178, 298, 268, 382,312, 399, 414, 533, 96, 161, 207, 275, 190, 295, 282, 393, 220, 308,321, 417, 335, 436, 449, 541, 241, 327, 344, 443, 355, 462, 470, 567,367, 481, 499, 587, 509, 614, 626, 738, 113, 188, 199, 302, 245, 315,334, 430, 229, 343, 353, 456, 366, 466, 483, 580, 271, 363, 376, 489,392, 472, 497, 600, 405, 521, 531, 619, 552, 649, 660, 759, 289, 391,401, 519, 422, 507, 537, 634, 438, 544, 571, 650, 582, 669, 685, 774,476, 562, 591, 680, 603, 691, 713, 788, 636, 706, 729, 810, 745, 820,842, 915, 148, 216, 264, 342, 233, 360, 369, 485, 285, 379, 394, 501,409, 525, 535, 627, 310, 402, 421, 511, 437, 554, 564, 652, 455, 550,578, 666, 602, 694, 709, 780, 320, 429, 448, 558, 459, 565, 586, 677,493, 589, 617, 697, 631, 715, 735, 804, 515, 615, 642, 718, 657, 731,748, 823, 674, 762, 771, 835, 790, 855, 872, 931, 325, 458, 487, 593,505, 612, 624, 719, 529, 622, 644, 739, 661, 758, 770, 833, 548, 653,672, 752, 688, 763, 784, 853, 704, 789, 798, 860, 813, 879, 889, 942,584, 676, 696, 778, 726, 792, 801, 868, 732, 811, 824, 886, 838, 895,904, 951, 751, 826, 843, 898, 859, 908, 916, 956, 869, 919, 928, 966,937, 976, 985, 1008, 179, 253, 278, 380, 318, 400, 418, 539, 305, 424,442, 556, 457, 575, 596, 689, 322, 450, 478, 573, 495, 598, 610, 710,517, 620, 639, 722, 655, 746, 753, 834, 329, 474, 491, 608, 523, 637,629, 734, 546, 647, 663, 749, 679, 773, 775, 851, 569, 668, 692, 766,703, 782, 796, 861, 724, 805, 812, 880, 825, 890, 901, 948, 354, 527,503, 645, 560, 671, 665, 767, 594, 683, 699, 786, 712, 793, 809, 876,607, 700, 716, 797, 744, 818, 827, 887, 755, 828, 840, 897, 857, 911,918, 962, 640, 721, 741, 819, 768, 846, 854, 905, 777, 841, 863, 913,874, 923, 934, 969, 800, 870, 881, 930, 893, 940, 925, 980, 902, 946,954, 973, 957, 989, 995, 1013, 375, 576, 543, 682, 605, 702, 707, 803,632, 728, 736, 821, 756, 832, 850, 907, 658, 742, 764, 829, 781, 852,865, 914, 794, 873, 862, 922, 888, 933, 939, 974, 686, 779, 760, 856,808, 867, 882, 926, 816, 885, 892, 943, 903, 936, 950, 982, 839, 896,909, 947, 917, 955, 964, 987, 924, 960, 970, 998, 977, 991, 1001, 1017,725, 785, 815, 883, 830, 891, 900, 945, 845, 910, 906, 958, 921, 952,965, 992, 864, 912, 927, 968, 935, 963, 979, 996, 944, 981, 971, 999,986, 1004, 1006, 1015, 877, 932, 941, 972, 953, 978, 983, 1002, 959,984, 994, 1009, 988, 1003, 1011, 1020, 967, 997, 990, 1007, 1000, 1014,1010, 1019, 1005, 1012, 1016, 1021, 1018).

In this example, the Z sequence is specifically: [1, 2, (5, 11, 3, 13,8, 25, 4, 16, 19, 29, 12, 34, 37, 71, 6, 18, 14, 31, 21, 40, 48, 77, 23,52, 42, 85, 58, 93, 100, 162, 7, 17, 22, 43, 26, 51, 47, 89, 30, 56, 63,97, 68, 108, 112, 170, 36, 60, 73, 111, 78, 120, 127, 185, 84, 130, 139,201, 149, 208, 226, 323, 9, 24, 27, 54, 35, 59, 67, 104, 38, 75, 61,114, 81, 124, 137, 194, 44, 70, 82, 129, 92, 132, 146, 206, 101, 150,159, 219, 172, 239, 251, 356, 53, 88, 98, 143, 109, 152, 163, 234, 116,165, 184, 250, 198, 259, 277, 378, 131, 192, 202, 269, 213, 280, 296,395, 232, 303, 319, 416, 339, 431, 464, 574, 15, 28, 41, 69, 32, 80, 74,133, 46, 83, 91, 144, 99, 156, 158, 227, 57, 95, 103, 153, 110, 168,183, 244, 125, 182, 193, 258, 205, 272, 288, 390, 62, 107, 122, 181,118, 186, 196, 270, 141, 204, 214, 281, 230, 301, 314, 411, 147, 217,235, 306, 248, 338, 348, 433, 266, 357, 364, 452, 386, 482, 498, 613,66, 119, 136, 203, 145, 215, 224, 304, 160, 221, 238, 332, 252, 340,358, 454, 173, 246, 265, 350, 279, 371, 383, 468, 293, 389, 406, 484,426, 518, 536, 641, 195, 273, 284, 373, 307, 396, 408, 508, 331, 419,432, 530, 460, 542, 557, 667, 341, 435, 465, 547, 480, 570, 588, 681,496, 590, 609, 698, 633, 727, 757, 844, 20, 39, 45, 86, 49, 94, 102,164, 55, 106, 115, 174, 123, 191, 200, 294, 65, 117, 126, 197, 140, 209,212, 297, 151, 218, 231, 317, 247, 337, 345, 445, 72, 134, 138, 210,154, 223, 236, 336, 169, 243, 254, 346, 263, 372, 374, 471, 177, 262,274, 368, 287, 385, 403, 486, 311, 412, 420, 510, 439, 528, 551, 654,79, 157, 167, 240, 176, 256, 267, 359, 189, 276, 283, 388, 299, 397,415, 514, 228, 291, 309, 413, 324, 423, 440, 532, 352, 441, 461, 545,479, 572, 585, 687, 255, 328, 347, 428, 365, 453, 473, 559, 377, 463,488, 581, 512, 597, 621, 708, 407, 500, 516, 611, 534, 625, 601, 740,553, 648, 670, 720, 678, 772, 791, 849, 90, 175, 187, 286, 222, 300,313, 410, 242, 316, 330, 434, 351, 446, 469, 563, 261, 349, 362, 444,384, 467, 492, 577, 398, 502, 504, 595, 524, 618, 630, 723, 290, 381,370, 475, 404, 494, 513, 604, 427, 522, 538, 628, 555, 638, 659, 747,451, 540, 566, 651, 579, 673, 693, 765, 599, 684, 711, 802, 730, 807,814, 878, 326, 387, 425, 520, 447, 526, 549, 643, 477, 568, 561, 664,592, 675, 695, 783, 490, 583, 606, 705, 623, 690, 737, 795, 646, 743,714, 817, 761, 831, 848, 899, 506, 616, 635, 717, 656, 733, 750, 822,662, 754, 787, 847, 769, 836, 871, 938, 701, 799, 776, 858, 806, 875,866, 929, 837, 884, 894, 949, 920, 961, 975, 993, 10, 33, 76, 121, 50,135, 105, 211, 64, 155, 171, 225, 128, 249, 257, 333, 87, 166, 142, 237,180, 260, 292, 361, 178, 298, 268, 382, 312, 399, 414, 533, 96, 161,207, 275, 190, 295, 282, 393, 220, 308, 321, 417, 335, 436, 449, 541,241, 327, 344, 443, 355, 462, 470, 567, 367, 481, 499, 587, 509, 614,626, 738, 113, 188, 199, 302, 245, 315, 334, 430, 229, 343, 353, 456,366, 466, 483, 580, 271, 363, 376, 489, 392, 472, 497, 600, 405, 521,531, 619, 552, 649, 660, 759, 289, 391, 401, 519, 422, 507, 537, 634,438, 544, 571, 650, 582, 669, 685, 774, 476, 562, 591, 680, 603, 691,713, 788, 636, 706, 729, 810, 745, 820, 842, 915, 148, 216, 264, 342,233, 360, 369, 485, 285, 379, 394, 501, 409, 525, 535, 627, 310, 402,421, 511, 437, 554, 564, 652, 455, 550, 578, 666, 602, 694, 709, 780,320, 429, 448, 558, 459, 565, 586, 677, 493, 589, 617, 697, 631, 715,735, 804, 515, 615, 642, 718, 657, 731, 748, 823, 674, 762, 771, 835,790, 855, 872, 931, 325, 458, 487, 593, 505, 612, 624, 719, 529, 622,644, 739, 661, 758, 770, 833, 548, 653, 672, 752, 688, 763, 784, 853,704, 789, 798, 860, 813, 879, 889, 942, 584, 676, 696, 778, 726, 792,801, 868, 732, 811, 824, 886, 838, 895, 904, 951, 751, 826, 843, 898,859, 908, 916, 956, 869, 919, 928, 966, 937, 976, 985, 1008, 179, 253,278, 380, 318, 400, 418, 539, 305, 424, 442, 556, 457, 575, 596, 689,322, 450, 478, 573, 495, 598, 610, 710, 517, 620, 639, 722, 655, 746,753, 834, 329, 474, 491, 608, 523, 637, 629, 734, 546, 647, 663, 749,679, 773, 775, 851, 569, 668, 692, 766, 703, 782, 796, 861, 724, 805,812, 880, 825, 890, 901, 948, 354, 527, 503, 645, 560, 671, 665, 767,594, 683, 699, 786, 712, 793, 809, 876, 607, 700, 716, 797, 744, 818,827, 887, 755, 828, 840, 897, 857, 911, 918, 962, 640, 721, 741, 819,768, 846, 854, 905, 777, 841, 863, 913, 874, 923, 934, 969, 800, 870,881, 930, 893, 940, 925, 980, 902, 946, 954, 973, 957, 989, 995, 1013,375, 576, 543, 682, 605, 702, 707, 803, 632, 728, 736, 821, 756, 832,850, 907, 658, 742, 764, 829, 781, 852, 865, 914, 794, 873, 862, 922,888, 933, 939, 974, 686, 779, 760, 856, 808, 867, 882, 926, 816, 885,892, 943, 903, 936, 950, 982, 839, 896, 909, 947, 917, 955, 964, 987,924, 960, 970, 998, 977, 991, 1001, 1017, 725, 785, 815, 883, 830, 891,900, 945, 845, 910, 906, 958, 921, 952, 965, 992, 864, 912, 927, 968,935, 963, 979, 996, 944, 981, 971, 999, 986, 1004, 1006, 1015, 877, 932,941, 972, 953, 978, 983, 1002, 959, 984, 994, 1009, 988, 1003, 1011,1020, 967, 997, 990, 1007, 1000, 1014, 1010, 1019, 1005, 1012, 1016,1021, 1018), 1022, 1023, 1024].

In the foregoing example sequences, locations of elements in thesubsequence L_(n) ^((m)) may be adjusted in the subsequence. Forexample, in an example (1) in Example 1, L₁ ^((m=3))=(5, 9, 3), and thenlocations of elements in a first subsequence L₁ ^((m=3)) in the sequencemay be adjusted to (5, 3, 9), (3, 5, 9), (3, 9, 5), (5, 9, 3), (9, 3,5), (9, 5, 3), or the like. A new sequence is obtained after theadjustment. In the foregoing specific sequences, an element set inparentheses represents the foregoing subsequence L_(n) ^((m)), andlocations of elements in the parentheses may be exchanged with eachother, but the locations of the elements in the parentheses cannot beexchanged with locations of elements outside the parentheses.

A process of performing polar coding based on a sequence in thisembodiment of this application is described below by using an example.

The sequence in this embodiment of this application meets a simplenesting characteristic, that is, another sequence with a relativelyshort mother code length may be obtained based on a sequence with arelatively long mother code length. Specifically, for example, asequence with a relatively short mother code length of N₂ is obtainedbased on a sequence with a relatively long mother code length of N₁.Elements whose sequence numbers are less than or equal to N₂ areextracted from the sequence with the relatively long mother code lengthof N₁, and an obtained subsequence is the sequence with the relativelyshort mother code length of N₂. An order of the elements in the obtainedsequence with the relatively short mother code length of N₂ is the sameas an order of these elements in the sequence with the relatively longmother code length of N₁. It is assumed that the to-be-coded bits with alength of K includes information bits with a length of K_(info) and acheck bit with a length of K_(CRC), a code length is M, and a mothercode length is N, where K=27, K_(info)=8, K_(CRC)=19, M=60, and N=64.When a parameter is constructed for a polar code, a sequence of N=64needs to be obtained.

It is assumed that the obtained sequence is a Q sequence. The Q sequencein the foregoing example sequences of N=64 may be directly used in thisembodiment of this application, or the Q sequence of N=64 may beobtained based on the nesting characteristic from Q sequences of N>64.For example, the Q sequence of N=128 in Example 1 is used. All sequencenumbers whose subchannel sequence numbers are less than or equal to 64are extracted, and an order of the obtained sequence numbers remainsunchanged to form a new sequence of N=64: [1, 2, (5, 9, 3), 17, 33, (7,4, 13, 6, 19, 10, 34, 18, 11), 21, 35, 25, (8, 37), (12, 41), (20, 14,49), 15, 22, (27, 36, 39, 23, 38, 26), 42, 29, (50, 43, 45, 16, 51, 24,53), (57, 28, 40), 30, (44, 31, 46), 52, 47, 54, (55, 58), 59, 61, 32,48, 56, 60, 62, 63, 64]. Locations of elements in some subsequences inthe sequence may be exchanged. Therefore, the new sequence of N=64obtained based on the nesting characteristic from the sequence of N=128is slightly different from the sequence of N=64 in the example (1) inExample 1: A range of parentheses is larger, and more sequences can beformed.

For example, the Q sequence of N=64 in the example (1) in Example 1 isdirectly obtained. Locations of K polarized channels are selected indescending order of reliability based on the obtained Q sequence, toplace the to-be-coded bits, where K=27. To be specific, the to-be-codedbits are placed at locations of polarized channels whose sequencenumbers are (43, 45, 16, 51, 24, 53, 57, 28, 40, 30, 44, 31, 46, 52, 47,54, 55, 58, 59, 61, 32, 48, 56, 60, 62, 63, 64) or at locations ofpolarized channels whose sequence numbers are (50, 45, 16, 51, 24, 53,57, 28, 40, 30, 44, 31, 46, 52, 47, 54, 55, 58, 59, 61, 32, 48, 56, 60,62, 63, 64). In the directly obtained Q sequence of N=64, locations oftwo elements (50, 43) in the subsequence=(50, 43) may be mutuallyexchanged. Therefore, there may be two possible combinations. Theto-be-coded bits are placed, with equal positions, in polarized channelscorresponding to the subsequences L₈ ^((m=2))=(16.51); L₉^((m=2))=(24.53); L₁₀ ^((m=2))=(57.28); L₁₁ ^((m=2))=(44.31). Therefore,whether to exchange elements does not need to be considered.

A prerequisite for the foregoing example of placing the information bitsis that sending priorities of the 27 to-be-coded bits are the same. Ifthe priorities of the to-be-coded bits are different, for example, 18check bits need to be placed at locations of 18 polarized channels withhighest reliability in the selected 27 polarized channels, and one checkbit needs to be placed at a location whose reliability is lower thanthat of some information bits. In this case, when the check bit isplaced, orders of the check bit in the four subsequences L₈ ^((m=2)) toL₁₁ ^((m=2)) may be considered. For example, the check bit needs to beplaced at a first location in L₈ ^((m=2)). When L₈ ^((m=2))=(16,51), thefirst location is 16, and after orders of 16 and 51 are exchanged, thefirst location is 51. Therefore, whether a location of 16 or a locationof 51 is selected for the check bit may affect final performance.

Locations other than locations at which the to-be-coded bits are placedare locations of frozen bits. Polar coding and rate matching areperformed based on the locations of the to-be-coded bits and thelocations of the frozen bits.

In addition, a new sequence of N=64 may be obtained based on the nestingcharacteristic by using the following sequences: a sequence of N=256, asequence of N=512, or a sequence of N=1024.

An example of N=64 is used for description above, and a coding method ofanother code length is similar to this. Details are not described hereinagain.

The sequences (1) to (30) in the foregoing examples in this embodimentof this application may be obtained by taking an intersection set ofseveral groups of sequences. For example, the sequence (1) in theforegoing example is obtained by taking an intersection set of severalgroups of sequences whose mother code lengths are 64. Certainly, thesequence may be obtained in another manner.

In a possible example, the following sequences S1 to S20 are obtainedthrough simulation. The sequences S1 to S20 are sequences whose mothercode lengths are 1024. Based on the nesting characteristic, sequenceswhose mother code lengths are 64, 128, 256, and 512 may be separatelyobtained based on the sequences S1 to S20, to obtain 20 groups ofsequences whose mother code lengths are separately 64, 128, 256, 512,and 1024. Sequences in examples (1) to (10) in Example 1 may be obtainedbased on a first group of sequences to a fifth group of sequences.Sequences in examples (11) to (20) in Example 2 may be obtained based onthe first group of sequences to a tenth group of sequences. Sequences inexamples (21) to (30) in Example 3 may be obtained based on the firstgroup of sequences to a twentieth group of sequences. It may beunderstood that a larger quantity of combined sequences indicates asmaller quantity of elements whose locations remain unchanged in anobtained sequence, a larger quantity of elements whose locations arechangeable, and a larger range of the obtained sequence.

In this embodiment of this application, the polar coding method shown inFIG. 2 may further be performed by using any one of the sequences S1 toS20.

Specifically, the sequences S1 to S20 may be as follows:

sequence S1: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 18, 129, 13,19, 34, 21, 35, 25, 257, 37, 66, 8, 67, 41, 12, 69, 130, 14, 49, 20,131, 513, 73, 15, 22, 36, 133, 81, 23, 26, 258, 38, 137, 97, 27, 259,39, 68, 42, 145, 29, 261, 70, 43, 50, 71, 161, 132, 265, 514, 45, 74,16, 51, 134, 515, 75, 273, 53, 82, 24, 193, 135, 517, 77, 83, 138, 57,289, 98, 28, 260, 40, 85, 139, 521, 146, 30, 99, 262, 44, 141, 147, 529,89, 321, 101, 31, 263, 72, 162, 266, 46, 52, 149, 163, 545, 105, 267,516, 47, 76, 274, 54, 153, 385, 165, 194, 136, 269, 518, 78, 113, 275,55, 84, 58, 290, 195, 577, 519, 79, 169, 277, 86, 140, 522, 59, 291,100, 197, 87, 142, 523, 177, 148, 281, 530, 61, 90, 293, 322, 102, 32,264, 641, 201, 143, 525, 150, 531, 91, 323, 103, 164, 297, 546, 106,268, 48, 209, 151, 533, 93, 325, 154, 386, 166, 547, 107, 270, 305, 114,276, 56, 225, 155, 537, 387, 769, 167, 549, 196, 329, 578, 109, 271,520, 80, 115, 170, 278, 60, 292, 157, 389, 198, 579, 337, 117, 171, 279,553, 88, 524, 178, 282, 62, 294, 199, 581, 393, 642, 173, 202, 144, 526,179, 561, 121, 353, 283, 532, 63, 92, 295, 324, 104, 298, 643, 203, 585,401, 527, 181, 210, 152, 285, 534, 94, 326, 299, 548, 108, 645, 306,205, 211, 593, 535, 95, 327, 185, 417, 226, 156, 538, 388, 770, 168,301, 550, 330, 110, 272, 307, 116, 213, 649, 158, 227, 609, 539, 390,771, 551, 331, 580, 111, 309, 338, 118, 172, 280, 554, 657, 217, 449,229, 159, 541, 391, 773, 200, 333, 582, 339, 119, 394, 174, 555, 180,313, 562, 122, 354, 284, 64, 296, 583, 673, 233, 341, 395, 644, 777,175, 557, 204, 586, 402, 528, 182, 563, 123, 286, 355, 300, 397, 646,206, 587, 241, 403, 785, 183, 565, 212, 345, 594, 125, 357, 287, 536,96, 328, 186, 418, 302, 705, 647, 308, 207, 589, 405, 214, 595, 650,187, 569, 419, 801, 228, 361, 610, 540, 772, 303, 552, 332, 112, 310,215, 597, 651, 409, 658, 189, 218, 421, 450, 230, 160, 542, 611, 392,774, 334, 369, 311, 340, 120, 556, 653, 314, 659, 219, 601, 451, 833,231, 613, 543, 775, 335, 584, 425, 674, 234, 342, 396, 778, 176, 558,315, 564, 124, 661, 356, 221, 453, 675, 235, 343, 617, 398, 779, 433,559, 588, 242, 404, 786, 184, 317, 566, 346, 126, 358, 288, 665, 897,677, 457, 706, 237, 399, 648, 781, 208, 590, 243, 625, 406, 787, 567,347, 596, 127, 359, 188, 570, 420, 802, 362, 304, 707, 465, 591, 245,407, 681, 789, 216, 349, 598, 652, 410, 190, 571, 422, 803, 363, 612,709, 370, 312, 599, 654, 689, 249, 481, 411, 660, 793, 191, 573, 220,423, 602, 805, 452, 834, 232, 365, 614, 544, 776, 336, 371, 426, 713,655, 316, 413, 662, 222, 603, 454, 835, 615, 373, 427, 676, 809, 236,344, 618, 780, 434, 560, 318, 721, 663, 223, 605, 455, 837, 666, 898,429, 678, 458, 238, 619, 400, 782, 435, 817, 244, 377, 626, 788, 319,568, 348, 128, 360, 737, 667, 899, 679, 459, 708, 841, 239, 621, 783,437, 466, 592, 246, 627, 408, 682, 790, 350, 572, 804, 669, 364, 901,461, 710, 467, 849, 247, 629, 683, 791, 351, 600, 441, 690, 250, 482,412, 794, 192, 574, 424, 806, 366, 711, 372, 469, 905, 685, 714, 656,691, 251, 633, 414, 483, 865, 795, 575, 604, 807, 836, 367, 616, 374,428, 810, 715, 913, 693, 473, 722, 253, 485, 415, 664, 797, 224, 606,456, 838, 375, 430, 811, 620, 436, 818, 717, 378, 320, 723, 607, 839,697, 929, 489, 738, 668, 900, 431, 680, 813, 460, 842, 240, 622, 784,438, 819, 379, 628, 725, 670, 739, 902, 462, 843, 497, 623, 439, 821,468, 850, 248, 381, 630, 684, 792, 352, 442, 729, 961, 741, 671, 903,463, 712, 845, 470, 851, 631, 906, 686, 443, 692, 825, 252, 634, 484,866, 796, 576, 808, 368, 471, 745, 853, 907, 687, 716, 914, 445, 694,474, 254, 635, 486, 416, 798, 867, 376, 812, 909, 718, 753, 915, 695,475, 724, 857, 255, 637, 487, 869, 799, 608, 840, 698, 930, 490, 432,814, 820, 719, 380, 917, 477, 726, 699, 931, 491, 740, 873, 815, 844,498, 624, 440, 822, 382, 727, 921, 701, 730, 933, 962, 493, 742, 672,904, 464, 846, 499, 881, 823, 852, 383, 632, 444, 826, 731, 963, 743,847, 501, 937, 472, 746, 854, 908, 688, 446, 827, 636, 868, 733, 965,747, 855, 910, 945, 505, 754, 916, 447, 696, 829, 476, 858, 256, 638,488, 870, 800, 969, 749, 911, 720, 755, 918, 478, 859, 639, 871, 700,932, 492, 874, 816, 977, 757, 919, 479, 728, 861, 922, 702, 934, 494,875, 500, 882, 824, 384, 761, 993, 923, 703, 732, 935, 964, 495, 744,877, 848, 502, 883, 938, 828, 925, 734, 966, 503, 885, 939, 748, 856,946, 506, 448, 830, 735, 967, 941, 970, 750, 912, 947, 507, 756, 889,831, 860, 640, 872, 971, 751, 949, 978, 509, 758, 920, 480, 862, 876,973, 979, 759, 863, 953, 762, 994, 924, 704, 936, 496, 878, 884, 981,763, 926, 995, 879, 504, 886, 940, 985, 765, 997, 927, 736, 968, 887,942, 948, 508, 890, 832, 1001, 943, 972, 752, 950, 510, 891, 974, 1009,951, 980, 511, 760, 893, 864, 954, 975, 982, 955, 764, 996, 880, 983,957, 986, 766, 998, 928, 888, 987, 767, 999, 1002, 944, 892, 989, 1003,1010, 952, 512, 894, 1005, 976, 1011, 895, 956, 1013, 984, 958, 1017,959, 988, 768, 1000, 990, 1004, 991, 1006, 1012, 896, 1007, 1014, 1015,1018, 960, 1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S2: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 75, 273,193, 521, 529, 71, 45, 132, 16, 74, 289, 545, 51, 24, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 72, 266, 46, 101, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 106, 322, 293, 201, 323,578, 150, 297, 48, 93, 209, 549, 579, 268, 386, 325, 305, 164, 151, 107,56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155, 276,60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278, 292,279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 123,394, 284, 64, 175, 341, 449, 354, 395, 233, 204, 673, 555, 557, 562,582, 296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644, 586,563, 300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589, 647,112, 540, 569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189, 552,610, 897, 160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597, 651,774, 658, 311, 120, 334, 219, 543, 611, 176, 392, 231, 314, 124, 340,335, 221, 451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 235, 288,453, 126, 342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559, 617,779, 675, 184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188, 588,566, 665, 625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787, 590,567, 648, 406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465, 802,420, 407, 245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422, 599,652, 612, 709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411, 232,249, 365, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 481,236, 223, 344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560, 834,805, 713, 835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455, 837,817, 676, 663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568, 619,666, 737, 899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667, 788,572, 783, 627, 679, 408, 364, 351, 437, 192, 247, 466, 412, 461, 250,366, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 441, 690,794, 604, 575, 467, 424, 372, 251, 414, 367, 469, 482, 374, 656, 901,806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606,483, 473, 224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 485, 430,456, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813,320, 622, 240, 431, 460, 379, 668, 839, 489, 438, 628, 623, 462, 381,439, 352, 497, 680, 725, 819, 842, 670, 738, 630, 468, 248, 442, 463,470, 443, 252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631,792, 845, 902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687,471, 416, 484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866,907, 716, 694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867,432, 380, 698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699,753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464,672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730,383, 499, 444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904,636, 826, 743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488,638, 505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 965, 858, 754,720, 916, 870, 478, 700, 749, 639, 816, 945, 755, 859, 911, 492, 479,728, 918, 871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919,757, 922, 875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848,935, 828, 734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885,939, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872,751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759,949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504,926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985,508, 890, 948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893,951, 864, 760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928,996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002,952, 1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988,1013, 1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S3: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 8, 130, 67, 513, 12, 41, 69, 20, 14,131, 49, 15, 73, 258, 22, 133, 36, 23, 259, 81, 26, 137, 38, 27, 514,97, 261, 39, 515, 265, 68, 42, 145, 29, 70, 43, 517, 50, 161, 273, 71,289, 545, 45, 193, 521, 529, 132, 74, 51, 134, 82, 75, 16, 24, 53, 321,135, 77, 57, 83, 28, 138, 98, 40, 385, 260, 85, 139, 262, 30, 146, 44,99, 516, 89, 141, 31, 147, 46, 263, 72, 266, 101, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 105, 274, 523, 641, 163, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 79, 277, 195, 290,59, 169, 86, 140, 100, 87, 197, 142, 291, 61, 281, 546, 769, 90, 102,148, 177, 91, 143, 533, 547, 537, 293, 201, 264, 32, 150, 322, 323, 578,103, 106, 93, 48, 297, 164, 151, 209, 549, 579, 386, 268, 305, 325, 107,154, 387, 166, 56, 329, 114, 520, 553, 642, 155, 80, 109, 225, 270, 167,524, 581, 561, 60, 276, 271, 115, 196, 170, 292, 278, 157, 88, 171, 117,279, 198, 62, 282, 526, 643, 532, 527, 178, 294, 389, 92, 585, 770, 199,144, 63, 121, 202, 283, 173, 104, 337, 179, 295, 94, 534, 645, 535, 593,548, 771, 298, 393, 324, 285, 203, 181, 108, 152, 210, 538, 95, 205,299, 401, 326, 353, 649, 609, 306, 301, 156, 211, 110, 168, 185, 116,226, 327, 158, 111, 773, 550, 657, 539, 551, 307, 213, 330, 118, 172,331, 227, 388, 309, 272, 580, 417, 217, 338, 159, 777, 119, 541, 554,280, 333, 390, 174, 122, 200, 180, 229, 394, 284, 391, 175, 313, 123,673, 555, 557, 562, 582, 354, 204, 64, 182, 339, 296, 449, 341, 286,395, 233, 125, 785, 705, 206, 183, 287, 528, 583, 644, 586, 563, 300,355, 212, 402, 186, 397, 241, 536, 587, 565, 646, 594, 207, 302, 801,345, 403, 328, 357, 308, 96, 418, 214, 187, 405, 112, 540, 569, 595,650, 772, 303, 833, 589, 647, 228, 361, 215, 189, 552, 610, 897, 332,310, 419, 409, 218, 450, 230, 160, 421, 542, 597, 651, 774, 658, 392,334, 311, 369, 340, 120, 314, 219, 543, 611, 335, 231, 234, 775, 659,613, 176, 124, 315, 556, 601, 653, 342, 221, 425, 451, 396, 778, 584,558, 674, 356, 288, 184, 235, 126, 343, 564, 661, 559, 617, 779, 675,317, 242, 346, 453, 398, 404, 208, 433, 358, 786, 188, 588, 566, 665,625, 781, 237, 127, 243, 399, 706, 347, 457, 359, 406, 304, 570, 596,190, 216, 677, 787, 590, 567, 648, 362, 707, 245, 349, 420, 407, 465,802, 410, 591, 681, 789, 571, 598, 312, 363, 573, 220, 422, 599, 652,612, 709, 602, 803, 370, 793, 191, 654, 689, 603, 249, 232, 411, 336,365, 423, 614, 660, 655, 316, 222, 371, 426, 236, 452, 481, 413, 344,223, 318, 544, 373, 615, 427, 776, 454, 238, 560, 834, 805, 713, 835,662, 809, 605, 618, 721, 780, 348, 319, 244, 434, 898, 455, 837, 817,676, 663, 360, 568, 619, 666, 737, 899, 841, 782, 626, 429, 377, 400,239, 458, 435, 128, 350, 246, 459, 592, 678, 621, 667, 788, 572, 783,627, 679, 437, 408, 466, 364, 247, 351, 412, 461, 250, 366, 600, 708,574, 669, 682, 790, 804, 791, 710, 683, 629, 467, 192, 441, 690, 794,604, 575, 372, 424, 251, 482, 469, 367, 414, 374, 656, 901, 806, 711,428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606, 483, 473,224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 430, 456, 722, 607,717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813, 485, 320, 622,431, 240, 379, 668, 839, 460, 438, 628, 623, 489, 381, 462, 497, 680,725, 819, 842, 670, 738, 630, 352, 439, 468, 248, 442, 463, 470, 443,252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631, 792, 845,902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687, 471, 416,484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866, 907, 716,694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867, 432, 380,698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699, 753, 840,915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464, 672, 930,844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730, 383, 499,444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904, 636, 826,743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488, 638, 505,800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720, 916, 870,478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492, 479, 728, 918,871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919, 757, 922,875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848, 935, 828,734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885, 939, 506,966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872, 751, 889,480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759, 949, 978,924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504, 926, 879,981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985, 508, 890,948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893, 951, 864,760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928, 996, 766,957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002, 952, 1003,894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013, 1000,1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015, 1018,1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S4: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 8, 130, 67, 12, 41, 69, 20, 514,14, 131, 49, 15, 73, 258, 22, 133, 36, 23, 259, 81, 26, 137, 38, 27,515, 97, 261, 39, 265, 68, 42, 145, 29, 70, 43, 50, 161, 273, 517, 71,289, 45, 193, 132, 74, 51, 134, 82, 75, 16, 521, 24, 53, 321, 135, 77,57, 83, 28, 138, 98, 529, 40, 385, 260, 85, 139, 262, 30, 146, 545, 44,99, 89, 141, 31, 147, 46, 263, 516, 72, 266, 101, 162, 52, 149, 47, 518,76, 267, 105, 274, 163, 54, 153, 577, 78, 269, 194, 165, 275, 55, 519,84, 136, 58, 113, 79, 277, 522, 195, 290, 59, 169, 86, 140, 523, 100,87, 197, 142, 291, 641, 61, 281, 90, 102, 148, 177, 530, 91, 143, 293,201, 264, 525, 32, 150, 322, 323, 531, 103, 106, 93, 48, 297, 546, 164,151, 209, 386, 769, 268, 305, 325, 107, 533, 154, 387, 166, 56, 329,547, 114, 155, 80, 537, 109, 225, 270, 167, 578, 60, 276, 271, 115, 549,196, 170, 292, 278, 520, 157, 88, 171, 642, 117, 279, 198, 62, 579, 282,178, 294, 524, 389, 92, 199, 144, 553, 63, 121, 202, 581, 283, 173, 104,532, 337, 179, 295, 526, 94, 298, 393, 643, 324, 285, 203, 561, 181,108, 152, 527, 210, 95, 205, 585, 299, 401, 326, 770, 353, 306, 534,301, 156, 211, 645, 110, 168, 185, 548, 116, 226, 535, 327, 158, 111,771, 307, 213, 593, 330, 118, 172, 538, 331, 227, 649, 388, 309, 272,550, 417, 217, 539, 338, 159, 609, 119, 280, 773, 333, 390, 174, 551,122, 200, 777, 180, 229, 580, 394, 284, 554, 391, 175, 657, 313, 123,541, 354, 204, 64, 582, 182, 339, 555, 296, 449, 562, 341, 286, 673,395, 785, 233, 125, 583, 206, 183, 801, 287, 300, 557, 355, 212, 705,402, 186, 644, 397, 241, 586, 207, 302, 563, 345, 646, 403, 328, 594,357, 308, 587, 96, 528, 418, 214, 536, 187, 405, 565, 112, 833, 303,228, 647, 361, 215, 589, 189, 569, 332, 310, 595, 419, 409, 540, 218,650, 450, 230, 610, 160, 552, 421, 392, 897, 334, 772, 311, 369, 597,340, 651, 120, 774, 314, 219, 542, 335, 658, 231, 234, 556, 176, 611,124, 315, 601, 342, 653, 221, 543, 425, 451, 659, 396, 558, 356, 775,288, 584, 184, 235, 778, 126, 613, 343, 674, 317, 242, 564, 346, 661,453, 559, 398, 588, 404, 208, 779, 433, 617, 358, 786, 188, 675, 237,566, 127, 665, 243, 399, 590, 347, 781, 457, 706, 359, 677, 406, 787,304, 567, 190, 596, 216, 648, 362, 570, 245, 349, 625, 420, 591, 407,789, 465, 707, 410, 802, 312, 571, 363, 681, 220, 598, 422, 652, 370,612, 191, 599, 249, 709, 232, 654, 411, 803, 336, 573, 365, 793, 423,316, 222, 602, 371, 614, 426, 660, 236, 689, 452, 603, 481, 655, 413,805, 344, 713, 223, 776, 318, 544, 373, 662, 427, 834, 454, 835, 238,615, 348, 618, 605, 319, 560, 244, 809, 434, 676, 455, 663, 360, 721,429, 898, 377, 780, 400, 817, 239, 837, 458, 619, 666, 435, 899, 128,678, 350, 568, 246, 841, 459, 626, 667, 437, 592, 408, 621, 466, 737,364, 782, 247, 679, 572, 351, 788, 412, 783, 461, 627, 708, 250, 682,366, 804, 467, 790, 192, 669, 600, 441, 683, 372, 629, 791, 424, 710,251, 574, 482, 794, 690, 469, 806, 367, 901, 604, 414, 711, 374, 656,428, 575, 633, 415, 714, 253, 795, 685, 483, 616, 473, 849, 691, 224,807, 606, 375, 810, 430, 905, 836, 456, 797, 378, 715, 693, 436, 620,664, 485, 722, 320, 607, 717, 431, 811, 913, 240, 838, 379, 865, 818,460, 813, 668, 438, 723, 622, 489, 680, 381, 697, 628, 462, 738, 839,497, 670, 623, 352, 819, 725, 439, 842, 630, 468, 684, 843, 248, 739,442, 900, 821, 463, 784, 929, 470, 729, 850, 671, 443, 631, 792, 252,845, 902, 368, 686, 634, 254, 712, 692, 471, 741, 906, 416, 796, 903,484, 687, 825, 635, 445, 866, 716, 376, 576, 694, 474, 851, 808, 961,486, 853, 798, 475, 907, 745, 255, 637, 718, 695, 432, 799, 812, 380,867, 724, 914, 487, 698, 909, 477, 753, 719, 814, 490, 857, 915, 840,440, 869, 820, 608, 491, 930, 726, 382, 699, 917, 624, 498, 815, 740,873, 493, 727, 701, 844, 464, 822, 931, 921, 383, 730, 962, 742, 499,672, 933, 904, 444, 846, 823, 881, 852, 446, 632, 826, 731, 472, 847,743, 746, 447, 688, 636, 827, 854, 256, 733, 937, 963, 476, 908, 868,800, 696, 501, 747, 638, 855, 829, 488, 754, 858, 965, 910, 505, 916,720, 945, 478, 870, 700, 749, 639, 755, 492, 911, 859, 969, 871, 479,918, 816, 702, 728, 384, 874, 757, 861, 932, 919, 494, 977, 922, 824,875, 732, 500, 934, 882, 703, 761, 495, 744, 923, 848, 877, 935, 828,502, 734, 883, 938, 748, 964, 448, 993, 925, 856, 735, 830, 885, 503,939, 966, 750, 860, 831, 756, 506, 946, 967, 872, 941, 889, 912, 507,751, 970, 947, 640, 862, 758, 971, 480, 949, 920, 978, 876, 759, 863,924, 509, 973, 762, 878, 979, 704, 953, 884, 936, 496, 763, 994, 981,879, 926, 886, 940, 927, 504, 765, 995, 985, 736, 887, 942, 968, 890,948, 997, 508, 832, 943, 752, 891, 972, 950, 1001, 893, 974, 1009, 864,510, 951, 980, 760, 954, 975, 982, 955, 764, 880, 766, 983, 928, 996,511, 957, 888, 986, 998, 987, 767, 944, 892, 999, 989, 1002, 952, 1003,894, 1010, 1005, 976, 512, 895, 1011, 956, 958, 984, 959, 768, 988,1013, 1000, 1017, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S5: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 257, 21, 35, 25, 66, 8, 37, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261,517, 38, 26, 97, 68, 265, 42, 145, 29, 70, 50, 75, 161, 43, 521, 273,193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 53, 321, 134, 77,83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44,99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577,76, 267, 105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525,84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100,140, 197, 87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143,91, 201, 546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 209,268, 386, 325, 305, 537, 769, 533, 164, 154, 151, 107, 56, 166, 387,578, 329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115,196, 170, 157, 88, 547, 62, 278, 292, 520, 279, 117, 171, 198, 642, 178,282, 92, 553, 202, 389, 294, 199, 524, 63, 144, 337, 585, 173, 283, 121,645, 104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210,285, 181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 156, 110, 534,401, 306, 301, 643, 211, 185, 327, 539, 116, 168, 593, 158, 226, 307,548, 330, 111, 771, 213, 118, 172, 551, 331, 227, 649, 388, 309, 159,609, 417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580,122, 200, 777, 180, 229, 554, 339, 657, 313, 541, 391, 175, 582, 394,284, 773, 123, 673, 555, 785, 64, 341, 705, 449, 562, 354, 801, 395,233, 204, 528, 583, 557, 296, 286, 182, 125, 206, 241, 644, 586, 563,287, 300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207,328, 646, 536, 403, 594, 187, 357, 589, 569, 308, 647, 419, 214, 302,228, 303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189,450, 332, 218, 160, 610, 597, 552, 651, 120, 230, 334, 409, 542, 774,611, 658, 311, 421, 601, 219, 369, 231, 653, 392, 176, 314, 340, 543,335, 124, 556, 775, 234, 315, 659, 613, 342, 778, 451, 221, 425, 356,674, 584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779,564, 404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588,781, 706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567,304, 598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220,648, 312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191,571, 370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365,423, 336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454,834, 318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434,560, 238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662,429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458,817, 246, 619, 350, 788, 128, 782, 898, 408, 667, 437, 592, 364, 621,466, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783,366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791,372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711,374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430,795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664,722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668,240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628,248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670,463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368,671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796,416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907,471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487,753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915,440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740,930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742,846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501,446, 933, 847, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638,908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800,700, 494, 505, 749, 945, 859, 874, 639, 755, 256, 969, 870, 492, 479,384, 911, 816, 918, 728, 871, 702, 932, 861, 500, 757, 732, 824, 923,875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 877, 502, 848,993, 448, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830,966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751,872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863,762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994,926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890,948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954,510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928,511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005,894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959,1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896,1014, 992, 1019, 960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S6: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11, 129,18, 13, 19, 34, 21, 35, 25, 66, 37, 258, 67, 8, 12, 130, 41, 69, 514,14, 20, 131, 49, 15, 73, 259, 22, 133, 36, 81, 23, 26, 137, 38, 97, 515,261, 145, 27, 39, 68, 42, 29, 161, 70, 265, 43, 50, 75, 517, 193, 71,45, 273, 132, 16, 74, 51, 24, 53, 289, 521, 134, 82, 77, 135, 28, 57,260, 83, 138, 40, 529, 98, 262, 30, 85, 139, 146, 31, 321, 545, 99, 44,89, 141, 263, 147, 72, 46, 516, 101, 266, 162, 52, 149, 47, 267, 769,76, 163, 105, 385, 54, 153, 78, 518, 194, 274, 165, 55, 84, 269, 577,136, 58, 113, 275, 195, 79, 519, 169, 290, 59, 86, 61, 277, 522, 87,140, 291, 100, 197, 523, 90, 281, 142, 177, 322, 91, 641, 102, 148, 293,143, 32, 530, 323, 103, 106, 264, 525, 201, 150, 48, 268, 93, 531, 209,386, 164, 151, 546, 297, 107, 56, 325, 533, 154, 225, 270, 114, 80, 547,276, 166, 109, 537, 387, 155, 60, 305, 578, 115, 167, 271, 157, 549,329, 196, 170, 278, 770, 198, 171, 389, 579, 117, 292, 88, 62, 520, 337,178, 63, 524, 279, 92, 282, 144, 642, 199, 393, 104, 553, 294, 173, 353,581, 202, 121, 401, 526, 179, 283, 94, 532, 152, 295, 203, 643, 324,108, 298, 561, 181, 210, 285, 527, 95, 417, 205, 585, 326, 185, 771,299, 211, 110, 534, 306, 156, 331, 645, 116, 449, 548, 111, 327, 168,593, 301, 213, 535, 388, 158, 272, 538, 226, 118, 649, 330, 172, 307,550, 227, 280, 609, 217, 309, 773, 159, 390, 657, 119, 338, 174, 539,333, 122, 551, 391, 200, 580, 180, 229, 554, 284, 123, 541, 313, 64,673, 339, 175, 394, 582, 233, 296, 777, 204, 354, 555, 182, 286, 562,341, 587, 206, 395, 705, 125, 402, 583, 183, 287, 557, 212, 355, 785,186, 300, 644, 207, 345, 528, 96, 397, 586, 187, 563, 403, 328, 536,241, 302, 565, 214, 801, 357, 112, 646, 418, 228, 594, 308, 589, 405,215, 647, 303, 189, 540, 332, 569, 160, 419, 772, 361, 218, 595, 310,650, 230, 409, 552, 334, 610, 120, 450, 774, 219, 542, 421, 176, 597,311, 651, 340, 658, 231, 392, 543, 314, 833, 124, 369, 611, 221, 556,451, 335, 601, 234, 653, 425, 775, 235, 315, 659, 342, 584, 126, 558,317, 613, 343, 184, 778, 396, 674, 356, 564, 242, 453, 661, 208, 559,346, 779, 398, 588, 188, 433, 675, 347, 617, 237, 897, 358, 566, 404,665, 127, 590, 399, 288, 706, 243, 786, 359, 677, 362, 567, 216, 596,457, 781, 406, 648, 190, 570, 304, 625, 349, 245, 787, 465, 707, 420,591, 407, 681, 220, 802, 363, 571, 312, 598, 191, 573, 410, 789, 481,599, 232, 652, 370, 803, 336, 612, 422, 709, 249, 602, 365, 793, 411,222, 316, 654, 371, 689, 423, 834, 236, 603, 413, 614, 452, 660, 426,805, 223, 655, 454, 544, 427, 835, 128, 615, 373, 618, 344, 776, 318,713, 238, 662, 560, 434, 780, 319, 605, 348, 721, 244, 898, 400, 676,455, 663, 360, 809, 429, 619, 239, 568, 458, 837, 666, 377, 737, 435,782, 246, 626, 350, 592, 408, 788, 678, 459, 621, 192, 899, 364, 667,437, 572, 466, 817, 627, 351, 679, 247, 783, 461, 669, 841, 441, 708,467, 682, 366, 790, 250, 710, 683, 412, 901, 372, 629, 804, 367, 600,424, 574, 251, 849, 690, 469, 575, 414, 791, 604, 482, 794, 374, 656,428, 711, 905, 253, 616, 483, 806, 685, 473, 865, 415, 714, 633, 375,913, 691, 224, 795, 430, 606, 664, 378, 807, 456, 715, 836, 436, 620,810, 485, 693, 379, 722, 797, 240, 607, 929, 320, 717, 431, 838, 697,489, 811, 723, 460, 622, 818, 438, 668, 462, 843, 628, 248, 961, 623,381, 839, 680, 439, 813, 725, 468, 900, 670, 442, 784, 738, 463, 630,352, 842, 684, 252, 819, 739, 443, 792, 729, 821, 497, 671, 902, 470,631, 850, 368, 686, 845, 484, 634, 903, 471, 712, 692, 445, 741, 796,416, 635, 825, 576, 254, 851, 687, 474, 906, 745, 486, 808, 716, 866,376, 694, 798, 475, 853, 718, 432, 907, 637, 914, 487, 695, 799, 380,724, 867, 698, 477, 812, 719, 490, 857, 608, 909, 255, 699, 915, 840,491, 753, 814, 726, 382, 869, 624, 440, 930, 740, 820, 498, 917, 727,815, 464, 701, 844, 672, 444, 931, 873, 730, 493, 822, 742, 921, 383,846, 632, 962, 499, 731, 933, 688, 823, 472, 852, 743, 904, 446, 826,636, 881, 501, 733, 963, 847, 746, 256, 937, 747, 827, 476, 854, 638,829, 855, 447, 696, 908, 868, 754, 488, 965, 720, 858, 910, 505, 700,945, 859, 478, 749, 870, 916, 639, 911, 492, 800, 755, 871, 874, 479,728, 969, 918, 702, 384, 816, 861, 757, 977, 932, 494, 919, 732, 875,824, 703, 500, 922, 993, 744, 882, 495, 848, 934, 761, 877, 923, 734,502, 828, 883, 935, 748, 925, 448, 964, 938, 735, 966, 939, 640, 503,885, 856, 830, 750, 946, 831, 506, 860, 756, 912, 967, 872, 941, 507,751, 970, 889, 947, 758, 862, 920, 509, 971, 704, 876, 949, 978, 863,759, 480, 973, 953, 979, 878, 762, 924, 884, 879, 496, 936, 763, 981,926, 994, 886, 940, 765, 504, 995, 985, 927, 887, 736, 942, 890, 968,948, 997, 508, 891, 752, 832, 943, 1001, 972, 950, 974, 760, 893, 951,510, 980, 954, 975, 864, 764, 955, 1009, 982, 880, 996, 983, 957, 928,511, 766, 986, 998, 888, 987, 944, 999, 892, 989, 1002, 767, 1003, 894,952, 1010, 976, 956, 512, 1005, 895, 1011, 984, 958, 1013, 768, 988,959, 1000, 1017, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 960, 1015,1018, 1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S7: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 65, 10, 11, 18, 13, 19,129, 34, 21, 35, 25, 8, 37, 66, 257, 67, 12, 41, 69, 14, 20, 49, 130,15, 73, 22, 131, 513, 36, 23, 133, 81, 26, 38, 27, 258, 137, 39, 68, 97,42, 259, 29, 145, 43, 70, 261, 50, 71, 16, 45, 74, 51, 265, 132, 161,514, 75, 24, 53, 134, 82, 515, 273, 77, 135, 83, 28, 57, 193, 138, 517,40, 98, 85, 260, 30, 139, 289, 521, 146, 99, 44, 31, 262, 141, 89, 147,72, 101, 46, 263, 529, 321, 52, 266, 162, 149, 47, 76, 105, 267, 54,163, 516, 274, 153, 545, 78, 55, 269, 136, 165, 84, 113, 58, 194, 275,518, 385, 79, 59, 86, 195, 140, 290, 169, 519, 277, 577, 522, 100, 87,32, 291, 61, 197, 142, 90, 523, 281, 148, 177, 102, 264, 143, 293, 530,91, 322, 201, 525, 150, 103, 48, 531, 106, 641, 323, 93, 268, 297, 164,151, 209, 154, 546, 107, 533, 325, 56, 270, 166, 114, 276, 155, 547,305, 386, 80, 109, 271, 537, 167, 115, 329, 60, 196, 225, 170, 520, 278,387, 157, 549, 578, 769, 88, 117, 292, 62, 171, 198, 279, 389, 579, 337,524, 282, 553, 178, 63, 199, 144, 294, 173, 92, 121, 202, 283, 581, 526,179, 393, 104, 295, 532, 561, 642, 324, 94, 203, 353, 298, 527, 285,152, 181, 585, 210, 108, 534, 643, 401, 95, 299, 326, 205, 211, 156,548, 306, 185, 535, 110, 645, 327, 272, 593, 301, 538, 168, 116, 330,226, 307, 213, 388, 158, 550, 417, 111, 539, 770, 649, 331, 118, 227,172, 280, 159, 551, 309, 390, 580, 338, 217, 609, 554, 771, 541, 119,333, 64, 200, 229, 174, 391, 122, 657, 339, 284, 555, 313, 582, 449,180, 394, 773, 296, 175, 562, 123, 204, 354, 233, 583, 341, 528, 286,395, 557, 182, 586, 563, 777, 644, 402, 96, 673, 355, 125, 300, 206,287, 183, 397, 587, 345, 212, 241, 186, 536, 403, 565, 646, 328, 207,357, 594, 302, 785, 589, 308, 187, 214, 418, 112, 647, 405, 595, 303,540, 569, 705, 650, 332, 361, 228, 215, 160, 552, 310, 419, 189, 218,610, 597, 772, 542, 651, 409, 801, 120, 334, 230, 311, 392, 421, 658,340, 219, 611, 369, 556, 314, 450, 543, 774, 653, 335, 601, 231, 176,124, 659, 234, 315, 584, 342, 451, 221, 613, 396, 558, 425, 775, 833,564, 778, 674, 356, 126, 235, 661, 343, 288, 559, 317, 453, 184, 398,588, 346, 617, 242, 779, 404, 566, 675, 433, 127, 208, 358, 237, 399,786, 665, 347, 590, 243, 457, 188, 567, 781, 648, 406, 677, 359, 596,304, 625, 570, 706, 787, 362, 897, 591, 349, 216, 245, 420, 190, 407,571, 598, 707, 465, 652, 410, 802, 681, 363, 789, 312, 191, 422, 220,612, 370, 249, 599, 544, 411, 803, 573, 709, 654, 336, 365, 602, 232,793, 423, 660, 689, 371, 316, 452, 222, 614, 481, 426, 776, 655, 413,805, 603, 834, 713, 236, 662, 344, 223, 615, 373, 560, 318, 427, 454,618, 835, 605, 780, 809, 676, 434, 128, 663, 238, 319, 455, 400, 721,429, 666, 348, 619, 377, 244, 458, 837, 568, 782, 435, 678, 360, 239,626, 788, 667, 817, 898, 592, 350, 459, 621, 246, 783, 408, 679, 437,627, 841, 572, 708, 466, 737, 682, 364, 790, 899, 669, 351, 247, 461,192, 250, 600, 467, 629, 412, 804, 574, 683, 441, 710, 791, 366, 901,849, 794, 424, 690, 372, 251, 482, 575, 711, 469, 656, 414, 806, 685,367, 604, 633, 714, 795, 691, 905, 224, 616, 374, 483, 253, 428, 415,807, 836, 606, 715, 473, 865, 810, 797, 664, 693, 375, 320, 456, 485,722, 430, 620, 378, 913, 607, 811, 838, 717, 436, 240, 723, 431, 668,818, 697, 379, 460, 622, 489, 839, 784, 813, 680, 438, 628, 842, 738,819, 725, 900, 670, 352, 929, 623, 381, 248, 462, 439, 843, 468, 630,739, 497, 684, 442, 792, 671, 821, 902, 463, 850, 729, 252, 631, 845,576, 443, 712, 470, 741, 686, 368, 903, 634, 851, 796, 825, 961, 692,906, 484, 254, 471, 416, 808, 687, 445, 635, 716, 474, 866, 745, 853,798, 907, 694, 376, 255, 486, 914, 608, 475, 867, 637, 812, 718, 799,695, 909, 857, 487, 724, 432, 753, 698, 380, 915, 490, 840, 719, 477,869, 814, 820, 699, 726, 930, 624, 382, 491, 917, 815, 440, 844, 873,740, 498, 727, 672, 822, 931, 701, 383, 464, 493, 730, 921, 632, 846,499, 444, 742, 823, 904, 933, 852, 731, 881, 826, 962, 847, 472, 743,501, 688, 446, 636, 746, 827, 854, 963, 733, 908, 937, 256, 447, 476,868, 638, 747, 505, 855, 800, 829, 965, 696, 910, 858, 488, 754, 916,945, 639, 720, 478, 870, 749, 911, 859, 755, 969, 700, 492, 918, 479,871, 816, 874, 861, 728, 757, 932, 702, 384, 919, 494, 977, 922, 875,500, 824, 703, 934, 495, 732, 882, 761, 923, 848, 877, 744, 502, 935,883, 828, 964, 734, 993, 938, 925, 503, 448, 748, 506, 856, 735, 885,830, 939, 966, 946, 640, 507, 750, 831, 967, 912, 941, 860, 889, 756,970, 947, 480, 872, 751, 509, 862, 971, 758, 920, 949, 978, 876, 863,759, 973, 704, 496, 762, 979, 924, 953, 878, 936, 884, 763, 994, 981,926, 879, 504, 736, 886, 995, 765, 940, 927, 985, 508, 887, 832, 968,997, 942, 890, 948, 752, 510, 943, 891, 972, 1001, 950, 511, 864, 893,760, 974, 951, 980, 1009, 954, 975, 764, 955, 982, 880, 996, 766, 983,928, 957, 986, 888, 767, 998, 987, 999, 944, 892, 1002, 989, 512, 894,1003, 952, 1010, 895, 976, 1005, 1011, 956, 984, 1013, 958, 768, 959,988, 1017, 1000, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 1015, 960,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S8: [1, 2, 3, 5, 9, 17, 33, 4, 6, 7, 65, 10, 11, 18, 13, 129,19, 34, 21, 35, 25, 257, 37, 8, 66, 67, 41, 12, 69, 14, 130, 49, 20, 15,73, 513, 131, 22, 133, 36, 23, 81, 26, 258, 38, 137, 27, 259, 39, 97,68, 42, 29, 145, 261, 70, 43, 50, 71, 265, 45, 16, 74, 514, 161, 132,51, 75, 515, 134, 273, 53, 24, 82, 77, 517, 135, 193, 83, 138, 57, 28,289, 260, 40, 98, 521, 139, 85, 30, 146, 262, 99, 141, 44, 31, 89, 529,147, 263, 321, 101, 72, 266, 46, 162, 149, 52, 267, 47, 105, 545, 76,516, 163, 274, 54, 153, 269, 385, 78, 518, 165, 136, 275, 194, 55, 113,84, 58, 79, 519, 577, 290, 195, 277, 522, 169, 140, 86, 59, 291, 197,100, 523, 87, 142, 281, 61, 32, 90, 530, 177, 148, 293, 264, 322, 102,525, 143, 201, 641, 91, 531, 150, 323, 103, 297, 268, 48, 106, 546, 164,93, 533, 151, 209, 325, 154, 270, 107, 547, 386, 166, 305, 276, 56, 114,537, 155, 271, 329, 769, 109, 549, 387, 80, 520, 167, 578, 225, 196,278, 115, 170, 157, 60, 579, 389, 292, 553, 279, 198, 524, 337, 171,117, 88, 282, 62, 178, 581, 294, 199, 393, 526, 173, 144, 283, 202, 642,63, 121, 561, 92, 532, 179, 295, 353, 324, 104, 527, 585, 298, 203, 643,285, 401, 94, 534, 181, 152, 210, 326, 299, 205, 108, 645, 548, 95, 535,593, 306, 211, 538, 327, 185, 156, 301, 272, 330, 770, 417, 110, 550,388, 168, 307, 226, 649, 213, 116, 539, 158, 331, 771, 111, 551, 609,580, 390, 227, 309, 554, 280, 338, 172, 118, 541, 159, 217, 657, 333,773, 391, 449, 582, 229, 555, 200, 339, 394, 119, 174, 313, 284, 64,122, 562, 180, 583, 296, 354, 777, 557, 395, 528, 341, 175, 586, 233,673, 204, 644, 286, 123, 563, 402, 182, 355, 587, 397, 300, 287, 206,646, 345, 785, 125, 565, 403, 96, 536, 183, 594, 241, 212, 357, 328,186, 589, 302, 207, 647, 705, 418, 595, 405, 308, 650, 569, 214, 540,187, 303, 361, 801, 332, 772, 419, 112, 552, 610, 228, 651, 597, 310,215, 409, 542, 189, 160, 218, 658, 334, 774, 611, 421, 392, 450, 311,230, 653, 556, 369, 340, 120, 543, 601, 314, 219, 659, 335, 775, 833,613, 451, 584, 231, 778, 425, 558, 396, 342, 176, 315, 234, 674, 221,124, 661, 564, 453, 356, 779, 559, 617, 343, 588, 398, 235, 675, 317,288, 346, 786, 433, 126, 566, 404, 184, 242, 665, 358, 781, 399, 457,897, 590, 237, 677, 208, 648, 347, 787, 706, 127, 567, 625, 596, 406,243, 570, 359, 188, 591, 304, 362, 802, 707, 420, 349, 789, 681, 407,652, 465, 598, 245, 571, 216, 410, 190, 363, 803, 709, 612, 422, 599,312, 654, 370, 793, 573, 411, 544, 191, 602, 249, 689, 220, 660, 365,805, 336, 776, 423, 834, 481, 614, 452, 232, 655, 371, 713, 426, 603,413, 316, 222, 662, 835, 615, 809, 454, 780, 427, 560, 373, 618, 344,236, 676, 605, 318, 223, 663, 721, 434, 837, 666, 455, 782, 619, 429,400, 458, 898, 319, 238, 678, 377, 817, 348, 788, 435, 128, 568, 626,244, 667, 360, 783, 841, 621, 459, 899, 592, 239, 679, 737, 708, 350,790, 627, 437, 682, 408, 466, 246, 669, 572, 461, 364, 901, 804, 351,791, 710, 849, 683, 629, 467, 600, 247, 794, 441, 574, 412, 192, 250,690, 366, 806, 711, 424, 482, 905, 685, 656, 469, 372, 795, 714, 575,633, 604, 414, 251, 691, 367, 807, 865, 836, 483, 616, 810, 715, 428,374, 797, 415, 473, 913, 606, 253, 693, 224, 664, 722, 838, 485, 811,456, 375, 717, 620, 430, 607, 320, 378, 818, 723, 436, 839, 697, 668,813, 784, 431, 842, 489, 929, 622, 460, 900, 240, 680, 379, 819, 738,725, 628, 438, 670, 843, 623, 462, 902, 739, 381, 821, 352, 792, 439,850, 684, 497, 630, 468, 248, 671, 729, 442, 845, 463, 903, 961, 741,712, 851, 906, 631, 686, 825, 470, 796, 443, 576, 634, 252, 692, 368,808, 866, 484, 907, 853, 687, 745, 471, 716, 798, 635, 445, 416, 474,914, 254, 694, 867, 486, 909, 812, 376, 799, 718, 857, 637, 475, 915,608, 255, 695, 753, 724, 869, 840, 698, 487, 814, 719, 432, 490, 930,477, 380, 917, 820, 726, 699, 815, 873, 844, 491, 931, 624, 740, 382,822, 727, 440, 498, 921, 701, 672, 730, 846, 493, 933, 464, 904, 962,383, 823, 742, 881, 852, 499, 632, 826, 731, 444, 847, 963, 743, 937,908, 854, 688, 501, 827, 746, 472, 733, 636, 446, 965, 868, 855, 910,747, 829, 800, 447, 858, 505, 945, 638, 476, 916, 256, 696, 754, 870,488, 911, 969, 749, 720, 859, 639, 478, 918, 755, 871, 700, 816, 874,492, 932, 861, 479, 919, 977, 757, 728, 922, 702, 875, 494, 934, 384,824, 882, 500, 923, 703, 761, 732, 877, 848, 495, 935, 993, 964, 744,883, 938, 502, 925, 828, 734, 966, 939, 885, 856, 503, 748, 830, 735,448, 506, 946, 967, 941, 912, 970, 831, 750, 889, 860, 507, 947, 640,756, 872, 971, 751, 862, 509, 949, 480, 920, 978, 758, 973, 876, 863,979, 759, 953, 924, 704, 762, 878, 496, 936, 994, 981, 884, 926, 763,879, 995, 940, 886, 504, 927, 985, 765, 736, 997, 968, 887, 942, 832,890, 508, 948, 943, 1001, 972, 752, 891, 510, 950, 974, 893, 864, 511,951, 1009, 980, 760, 954, 975, 982, 955, 764, 880, 996, 983, 957, 928,986, 766, 998, 888, 987, 767, 999, 944, 1002, 989, 892, 1003, 894, 512,952, 1010, 1005, 976, 895, 1011, 956, 1013, 984, 958, 959, 1017, 988,768, 1000, 990, 1004, 991, 1006, 896, 1012, 1007, 1014, 1015, 960, 1018,1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S9: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 41, 130, 12, 69, 49, 14,131, 20, 15, 73, 258, 22, 133, 23, 81, 36, 259, 26, 137, 97, 261, 38,145, 27, 514, 39, 515, 265, 68, 29, 42, 161, 43, 45, 517, 50, 70, 273,193, 521, 529, 16, 71, 132, 74, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 105, 267, 163, 274, 523, 641, 76, 54, 153, 113, 269,194, 165, 275, 78, 55, 530, 525, 531, 136, 58, 84, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 48, 322, 293, 201, 323,578, 150, 297, 93, 106, 209, 549, 579, 268, 386, 325, 305, 164, 151, 56,107, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155,276, 60, 271, 115, 167, 524, 581, 561, 88, 196, 62, 157, 170, 278, 292,279, 198, 171, 117, 178, 282, 526, 643, 532, 527, 92, 63, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 175,394, 284, 123, 233, 341, 449, 354, 395, 204, 182, 673, 555, 557, 562,582, 296, 286, 125, 183, 206, 785, 705, 64, 287, 528, 583, 644, 586,563, 300, 355, 186, 402, 212, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589, 647,112, 540, 569, 595, 650, 772, 160, 418, 332, 228, 405, 310, 215, 552,610, 897, 120, 189, 361, 419, 409, 369, 218, 450, 421, 542, 597, 651,774, 658, 311, 230, 334, 219, 543, 611, 176, 392, 124, 314, 231, 340,335, 221, 451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 126, 288,184, 342, 396, 356, 778, 584, 558, 674, 343, 235, 564, 661, 559, 617,779, 675, 398, 317, 346, 242, 208, 404, 358, 188, 237, 786, 127, 588,566, 665, 625, 781, 304, 453, 433, 243, 347, 706, 399, 677, 787, 590,567, 648, 216, 406, 359, 570, 596, 362, 707, 190, 457, 349, 420, 802,407, 245, 410, 363, 591, 681, 789, 571, 598, 220, 573, 422, 370, 599,652, 612, 709, 602, 803, 312, 793, 191, 411, 654, 689, 603, 232, 249,365, 465, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 236,223, 344, 373, 427, 544, 481, 615, 454, 776, 318, 238, 434, 560, 834,805, 713, 835, 662, 809, 605, 618, 721, 780, 348, 898, 319, 455, 837,817, 676, 663, 244, 429, 400, 360, 239, 377, 458, 435, 350, 568, 619,666, 737, 899, 841, 782, 626, 246, 459, 408, 592, 678, 621, 667, 788,572, 783, 627, 679, 128, 364, 351, 247, 437, 466, 412, 461, 250, 366,467, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 424, 690,794, 604, 575, 192, 372, 441, 251, 414, 367, 469, 482, 374, 656, 901,806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606,224, 375, 483, 664, 836, 905, 810, 715, 620, 797, 693, 430, 456, 473,378, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 436, 320, 813,240, 622, 431, 485, 460, 379, 668, 839, 438, 489, 628, 623, 462, 381,439, 352, 248, 680, 725, 819, 842, 670, 738, 630, 468, 442, 252, 463,497, 443, 368, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631,792, 845, 902, 686, 470, 634, 712, 471, 692, 741, 851, 825, 903, 687,416, 484, 254, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866,907, 716, 694, 808, 475, 798, 637, 695, 432, 718, 576, 799, 812, 867,380, 487, 698, 914, 255, 724, 909, 857, 719, 477, 814, 608, 490, 699,753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 464, 383, 498,672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730,444, 493, 499, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904,636, 826, 743, 852, 847, 733, 963, 937, 827, 746, 476, 501, 638, 488,505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720, 916,870, 700, 749, 639, 816, 965, 945, 755, 859, 911, 256, 478, 492, 479,728, 918, 871, 494, 874, 702, 969, 500, 861, 495, 932, 919, 757, 922,875, 732, 934, 882, 824, 703, 502, 923, 384, 744, 761, 877, 977, 848,935, 828, 734, 883, 938, 964, 925, 748, 735, 856, 885, 939, 993, 448,503, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872,751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759,949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504,926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985,508, 890, 948, 832, 752, 943, 997, 972, 891, 950, 1001, 974, 893, 510,951, 864, 760, 511, 980, 954, 764, 975, 1009, 955, 880, 982, 983, 928,996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 989, 1002, 952,1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988, 1013,1000, 1017, 512, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S10: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11, 18,129, 13, 19, 34, 21, 35, 25, 37, 66, 258, 8, 67, 41, 12, 69, 130, 514,14, 49, 20, 73, 131, 15, 259, 22, 133, 36, 81, 23, 26, 137, 38, 27, 515,261, 97, 39, 68, 42, 145, 29, 70, 43, 265, 50, 71, 161, 517, 45, 74,132, 273, 16, 51, 75, 134, 53, 82, 289, 521, 24, 193, 77, 135, 83, 138,260, 57, 28, 98, 529, 139, 262, 40, 85, 146, 30, 99, 321, 545, 141, 44,89, 147, 263, 31, 101, 72, 516, 162, 266, 46, 149, 52, 105, 267, 769,163, 47, 76, 274, 153, 54, 165, 518, 194, 385, 78, 113, 136, 269, 577,55, 84, 58, 275, 195, 79, 519, 169, 290, 140, 86, 59, 277, 522, 197,100, 291, 87, 142, 523, 177, 281, 61, 90, 293, 148, 530, 32, 201, 322,102, 143, 641, 264, 91, 150, 323, 525, 103, 106, 164, 297, 209, 531, 48,268, 93, 151, 546, 325, 154, 107, 386, 533, 166, 114, 270, 155, 56, 547,305, 225, 109, 537, 276, 167, 196, 329, 549, 80, 115, 387, 170, 578,271, 157, 60, 278, 770, 198, 171, 389, 520, 117, 292, 88, 178, 579, 337,62, 199, 553, 279, 173, 282, 202, 524, 121, 393, 144, 581, 294, 179,283, 642, 63, 92, 353, 526, 203, 295, 104, 561, 181, 324, 210, 532, 298,94, 401, 585, 152, 205, 285, 643, 108, 326, 211, 527, 299, 95, 771, 306,185, 156, 534, 327, 226, 417, 645, 110, 301, 548, 168, 330, 213, 593,388, 116, 535, 272, 158, 307, 538, 227, 111, 649, 331, 172, 390, 550,217, 309, 539, 118, 338, 773, 159, 280, 609, 229, 449, 200, 551, 333,119, 580, 391, 174, 554, 122, 180, 657, 339, 64, 541, 394, 233, 582,313, 175, 284, 555, 204, 354, 777, 123, 395, 562, 182, 296, 583, 341,673, 206, 402, 557, 241, 286, 586, 125, 355, 644, 183, 397, 785, 212,300, 528, 96, 345, 563, 186, 403, 587, 207, 646, 287, 357, 565, 214,328, 594, 187, 801, 418, 228, 536, 302, 112, 705, 405, 589, 308, 215,647, 361, 189, 595, 419, 650, 218, 303, 772, 332, 160, 569, 409, 540,230, 310, 610, 421, 651, 219, 450, 774, 120, 552, 334, 231, 597, 369,658, 392, 542, 234, 311, 611, 340, 833, 176, 314, 653, 221, 556, 451,335, 601, 124, 659, 425, 775, 235, 396, 543, 342, 613, 242, 584, 315,674, 453, 126, 778, 356, 558, 343, 661, 184, 398, 564, 237, 617, 433,779, 317, 675, 208, 346, 559, 404, 588, 243, 786, 288, 665, 457, 566,127, 677, 358, 399, 706, 188, 897, 347, 590, 406, 625, 245, 648, 359,781, 362, 567, 216, 596, 420, 570, 465, 190, 787, 304, 707, 349, 591,407, 681, 249, 802, 410, 652, 363, 598, 191, 571, 422, 789, 370, 709,220, 612, 411, 803, 312, 599, 481, 654, 232, 689, 365, 793, 423, 222,452, 573, 336, 602, 371, 805, 236, 660, 426, 544, 413, 713, 316, 834,223, 614, 454, 655, 427, 776, 238, 603, 373, 662, 344, 835, 434, 615,244, 618, 676, 318, 809, 455, 721, 429, 560, 128, 780, 458, 605, 377,663, 400, 837, 435, 666, 239, 619, 319, 898, 678, 348, 626, 459, 782,246, 667, 360, 568, 437, 817, 737, 466, 621, 247, 788, 350, 679, 408,708, 461, 841, 592, 364, 627, 250, 899, 467, 682, 783, 351, 669, 441,572, 412, 790, 192, 710, 683, 482, 901, 366, 629, 804, 424, 600, 469,690, 251, 849, 574, 372, 711, 414, 791, 685, 483, 794, 367, 714, 428,633, 905, 253, 656, 473, 806, 691, 374, 795, 415, 575, 604, 485, 865,715, 224, 807, 456, 616, 693, 375, 836, 430, 722, 810, 378, 606, 913,436, 664, 320, 717, 797, 240, 620, 838, 489, 723, 431, 811, 607, 460,818, 697, 379, 668, 839, 438, 738, 462, 929, 622, 248, 813, 680, 497,842, 725, 381, 900, 628, 439, 784, 670, 468, 819, 739, 352, 623, 442,843, 684, 252, 902, 729, 463, 821, 630, 850, 470, 671, 792, 443, 741,961, 484, 712, 845, 368, 631, 903, 471, 686, 634, 445, 692, 851, 474,576, 906, 745, 254, 825, 687, 416, 796, 716, 486, 866, 635, 907, 475,694, 808, 376, 853, 718, 487, 914, 753, 798, 490, 637, 867, 432, 695,909, 724, 477, 812, 608, 380, 857, 698, 915, 255, 719, 799, 869, 491,726, 840, 699, 498, 930, 740, 382, 814, 624, 917, 440, 820, 727, 873,493, 701, 931, 730, 464, 815, 844, 672, 499, 921, 742, 822, 383, 933,731, 962, 444, 632, 846, 743, 881, 501, 904, 746, 823, 472, 852, 688,826, 446, 733, 963, 847, 636, 256, 937, 747, 908, 505, 854, 754, 827,965, 447, 638, 868, 855, 696, 476, 910, 749, 945, 829, 488, 720, 858,916, 478, 755, 800, 969, 639, 870, 492, 911, 700, 859, 918, 479, 757,871, 874, 728, 494, 932, 977, 702, 816, 861, 500, 919, 761, 922, 875,703, 384, 934, 882, 732, 923, 495, 824, 993, 744, 877, 935, 734, 502,964, 848, 883, 748, 938, 503, 925, 828, 735, 966, 939, 750, 506, 885,856, 946, 756, 830, 967, 448, 941, 640, 970, 889, 912, 947, 507, 751,831, 860, 971, 758, 872, 949, 509, 978, 759, 862, 920, 973, 876, 762,480, 979, 863, 953, 924, 704, 994, 878, 936, 496, 981, 763, 884, 926,995, 879, 940, 765, 504, 985, 886, 927, 997, 736, 968, 887, 942, 890,948, 508, 832, 752, 1001, 943, 972, 891, 950, 974, 760, 1009, 893, 510,951, 980, 864, 954, 764, 975, 982, 955, 996, 880, 983, 957, 986, 511,766, 928, 998, 987, 888, 999, 1002, 944, 989, 892, 767, 1003, 1010, 894,952, 1005, 976, 512, 1011, 895, 956, 1013, 984, 958, 768, 1017, 959,988, 1000, 990, 1004, 991, 1006, 1012, 896, 1007, 1014, 1015, 1018, 960,1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S11: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 65, 10, 11, 18, 13, 19,129, 34, 21, 35, 25, 8, 37, 66, 257, 67, 12, 41, 69, 14, 20, 49, 130,15, 73, 131, 22, 513, 36, 23, 133, 81, 26, 38, 27, 258, 137, 39, 68, 97,42, 259, 29, 145, 43, 70, 261, 50, 71, 16, 45, 74, 51, 265, 132, 161,514, 75, 24, 53, 134, 82, 515, 273, 77, 135, 83, 28, 57, 193, 138, 517,40, 98, 85, 260, 139, 30, 289, 521, 146, 99, 44, 31, 262, 141, 89, 147,72, 101, 46, 263, 529, 321, 52, 266, 162, 149, 47, 76, 105, 267, 163,54, 516, 274, 153, 545, 78, 55, 269, 136, 165, 84, 113, 58, 194, 275,518, 385, 79, 59, 195, 86, 140, 290, 169, 519, 277, 577, 522, 100, 87,32, 291, 61, 197, 142, 90, 523, 281, 148, 177, 102, 264, 143, 293, 530,91, 322, 201, 525, 150, 103, 48, 531, 106, 641, 323, 93, 268, 297, 164,151, 209, 154, 546, 107, 533, 325, 56, 270, 166, 114, 276, 155, 547,305, 386, 80, 109, 271, 537, 167, 115, 329, 60, 196, 225, 170, 520, 387,278, 157, 549, 578, 769, 88, 117, 292, 171, 62, 198, 279, 389, 579, 337,524, 282, 553, 178, 63, 199, 144, 294, 173, 92, 121, 202, 283, 581, 526,179, 393, 104, 295, 532, 561, 642, 324, 203, 94, 353, 298, 527, 285,152, 181, 585, 210, 108, 643, 534, 401, 95, 299, 326, 205, 211, 156,548, 306, 185, 535, 110, 645, 327, 272, 593, 301, 538, 168, 116, 330,226, 307, 213, 388, 158, 550, 417, 111, 539, 770, 649, 331, 227, 118,172, 280, 159, 551, 309, 390, 580, 338, 217, 609, 554, 771, 541, 119,333, 64, 200, 229, 174, 391, 122, 657, 339, 284, 555, 313, 582, 449,180, 394, 773, 296, 175, 562, 123, 204, 354, 233, 583, 341, 528, 395,286, 557, 182, 586, 563, 777, 644, 402, 96, 673, 355, 125, 300, 206,287, 183, 397, 587, 345, 212, 241, 186, 536, 403, 565, 646, 328, 207,357, 594, 302, 785, 589, 308, 187, 214, 418, 112, 647, 405, 595, 303,540, 569, 705, 650, 332, 361, 228, 215, 160, 552, 419, 310, 189, 218,610, 597, 772, 651, 542, 409, 801, 120, 334, 230, 311, 392, 421, 658,340, 219, 611, 369, 556, 314, 450, 543, 774, 653, 335, 601, 231, 176,124, 659, 234, 315, 584, 451, 342, 221, 613, 396, 558, 425, 775, 833,564, 778, 674, 356, 235, 126, 661, 343, 288, 559, 317, 453, 184, 398,588, 346, 617, 242, 779, 404, 675, 566, 433, 127, 208, 358, 237, 399,786, 665, 347, 590, 243, 457, 188, 567, 781, 648, 406, 677, 359, 596,304, 625, 570, 706, 787, 362, 897, 591, 349, 216, 245, 420, 190, 407,571, 707, 598, 465, 652, 410, 802, 681, 363, 789, 312, 191, 422, 220,612, 370, 249, 599, 544, 411, 803, 573, 709, 654, 336, 365, 602, 232,793, 423, 660, 689, 371, 316, 452, 222, 614, 481, 426, 776, 655, 413,805, 603, 834, 713, 236, 662, 344, 223, 615, 373, 560, 427, 318, 454,618, 835, 605, 780, 809, 676, 434, 128, 663, 238, 319, 455, 400, 721,429, 666, 348, 619, 377, 244, 458, 837, 568, 782, 435, 678, 360, 239,626, 788, 667, 817, 898, 592, 459, 350, 621, 246, 783, 408, 679, 437,627, 841, 572, 708, 466, 737, 682, 364, 899, 790, 669, 351, 247, 461,192, 250, 600, 467, 629, 412, 804, 683, 574, 441, 710, 791, 366, 901,849, 794, 424, 690, 372, 251, 482, 575, 711, 469, 656, 414, 806, 685,367, 604, 633, 714, 795, 691, 905, 224, 616, 483, 374, 253, 428, 415,807, 836, 715, 606, 473, 865, 810, 797, 664, 693, 375, 320, 456, 485,722, 430, 620, 378, 913, 607, 811, 838, 717, 436, 240, 723, 431, 668,818, 697, 379, 460, 622, 489, 839, 784, 813, 680, 438, 628, 842, 738,819, 725, 900, 670, 352, 929, 623, 381, 248, 462, 439, 843, 468, 739,630, 497, 684, 442, 792, 671, 821, 902, 463, 850, 729, 252, 631, 845,576, 443, 712, 470, 741, 686, 368, 903, 634, 851, 796, 825, 961, 692,906, 484, 254, 471, 416, 808, 687, 445, 635, 716, 474, 866, 745, 853,907, 798, 694, 376, 255, 486, 914, 608, 475, 867, 637, 812, 718, 799,695, 909, 857, 487, 724, 432, 753, 698, 380, 915, 490, 840, 719, 477,869, 814, 820, 699, 726, 930, 624, 491, 382, 917, 815, 440, 844, 873,740, 498, 727, 672, 931, 822, 701, 383, 464, 493, 730, 921, 632, 846,499, 444, 742, 823, 904, 933, 852, 731, 881, 826, 962, 847, 472, 743,501, 688, 446, 636, 746, 827, 963, 854, 733, 908, 937, 256, 447, 476,868, 747, 638, 505, 855, 800, 829, 965, 696, 910, 858, 488, 754, 916,945, 639, 720, 478, 870, 749, 911, 859, 755, 969, 700, 492, 918, 479,871, 816, 874, 861, 728, 757, 932, 702, 384, 919, 494, 977, 922, 875,500, 824, 703, 934, 495, 732, 882, 761, 923, 848, 877, 744, 502, 935,883, 828, 964, 734, 993, 938, 925, 503, 448, 748, 506, 856, 735, 885,939, 830, 966, 946, 640, 507, 750, 831, 967, 912, 941, 860, 889, 756,970, 947, 480, 872, 751, 509, 971, 862, 758, 920, 949, 978, 876, 863,759, 973, 704, 496, 762, 979, 924, 953, 878, 936, 884, 763, 994, 981,926, 879, 504, 736, 995, 886, 765, 940, 927, 985, 508, 887, 832, 968,997, 942, 890, 948, 752, 510, 943, 891, 972, 1001, 950, 511, 864, 893,760, 974, 951, 980, 1009, 954, 975, 764, 955, 982, 880, 996, 766, 983,928, 957, 986, 888, 767, 998, 987, 999, 944, 892, 1002, 989, 512, 1003,894, 952, 1010, 895, 976, 1005, 1011, 956, 984, 1013, 958, 768, 959,988, 1017, 1000, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 1015, 960,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S12: [1, 2, 3, 5, 9, 17, 4, 33, 6, 7, 10, 65, 11, 18, 13, 19,129, 21, 34, 35, 25, 8, 37, 66, 257, 12, 67, 41, 14, 69, 20, 49, 15,130, 73, 22, 131, 23, 36, 513, 133, 26, 81, 38, 27, 137, 39, 258, 29,68, 42, 97, 259, 43, 145, 70, 261, 50, 16, 71, 45, 74, 51, 265, 132,161, 75, 24, 53, 514, 134, 82, 77, 515, 273, 135, 28, 83, 57, 138, 40,193, 517, 30, 85, 98, 139, 260, 289, 31, 44, 521, 99, 146, 141, 89, 262,147, 72, 46, 101, 263, 52, 529, 47, 266, 149, 321, 162, 76, 105, 54,267, 163, 153, 78, 55, 516, 274, 545, 269, 136, 84, 165, 58, 113, 79,275, 194, 518, 59, 385, 86, 140, 195, 169, 519, 277, 290, 32, 87, 61,522, 100, 577, 142, 291, 197, 90, 523, 281, 148, 177, 102, 143, 91, 264,293, 530, 48, 201, 525, 103, 150, 322, 93, 531, 106, 268, 151, 323, 297,164, 641, 107, 154, 56, 209, 533, 546, 270, 325, 166, 114, 155, 80, 276,109, 547, 305, 271, 167, 60, 386, 537, 115, 157, 329, 196, 170, 520,278, 225, 549, 387, 88, 62, 117, 578, 171, 279, 292, 198, 769, 63, 524,389, 282, 579, 337, 553, 178, 144, 199, 92, 173, 121, 294, 283, 202,526, 179, 104, 581, 393, 295, 94, 532, 203, 561, 527, 285, 152, 324,298, 181, 353, 642, 95, 108, 585, 210, 534, 299, 205, 643, 401, 326,156, 211, 185, 535, 110, 548, 306, 272, 327, 301, 168, 645, 538, 116,593, 111, 158, 330, 307, 213, 226, 550, 388, 539, 417, 118, 159, 331,172, 280, 649, 227, 551, 309, 770, 64, 217, 390, 541, 119, 580, 338,554, 609, 333, 200, 771, 174, 229, 122, 391, 284, 339, 555, 313, 180,657, 582, 175, 394, 123, 296, 449, 773, 204, 562, 528, 286, 233, 583,341, 557, 182, 354, 395, 96, 125, 586, 563, 287, 300, 206, 777, 183,355, 644, 402, 673, 397, 587, 345, 212, 186, 536, 241, 207, 565, 403,328, 302, 357, 646, 594, 187, 112, 589, 308, 214, 785, 303, 647, 540,405, 418, 595, 569, 160, 332, 215, 189, 361, 650, 228, 552, 310, 705,419, 218, 542, 120, 597, 610, 651, 409, 334, 311, 772, 230, 801, 219,392, 543, 340, 556, 421, 314, 611, 369, 658, 335, 176, 653, 231, 124,450, 601, 774, 315, 221, 659, 234, 584, 342, 558, 396, 613, 451, 425,775, 126, 564, 288, 235, 343, 559, 317, 778, 184, 356, 661, 833, 674,398, 127, 588, 453, 346, 617, 242, 208, 566, 779, 404, 237, 675, 433,358, 399, 347, 188, 665, 590, 243, 567, 786, 304, 457, 781, 359, 648,406, 596, 677, 570, 625, 591, 349, 216, 787, 190, 362, 245, 706, 407,420, 571, 897, 598, 191, 363, 652, 410, 312, 707, 465, 681, 789, 802,220, 544, 249, 422, 599, 573, 612, 370, 411, 336, 365, 654, 232, 803,709, 602, 423, 316, 222, 793, 371, 660, 689, 614, 655, 413, 452, 426,603, 776, 481, 805, 223, 236, 344, 560, 318, 713, 615, 373, 662, 834,427, 128, 454, 605, 618, 319, 780, 663, 835, 238, 809, 676, 434, 400,455, 348, 429, 619, 377, 666, 244, 568, 721, 239, 458, 782, 435, 360,837, 678, 626, 667, 592, 350, 788, 621, 246, 459, 817, 783, 408, 679,572, 437, 898, 627, 351, 192, 364, 669, 841, 247, 708, 466, 682, 790,737, 461, 899, 250, 600, 574, 412, 629, 467, 683, 441, 791, 366, 804,710, 251, 424, 575, 901, 794, 372, 849, 690, 367, 656, 414, 711, 604,469, 685, 482, 633, 806, 224, 795, 253, 714, 691, 616, 374, 415, 428,905, 483, 807, 606, 320, 715, 473, 797, 375, 664, 836, 810, 693, 865,456, 430, 607, 620, 485, 378, 722, 240, 811, 717, 436, 913, 838, 431,379, 668, 723, 697, 622, 460, 818, 784, 489, 839, 813, 680, 438, 628,352, 623, 381, 670, 842, 248, 819, 725, 738, 462, 439, 900, 929, 630,671, 843, 468, 684, 442, 792, 739, 497, 463, 821, 252, 576, 729, 902,631, 850, 443, 368, 845, 712, 470, 686, 741, 634, 903, 796, 851, 254,825, 692, 416, 471, 687, 445, 906, 484, 635, 808, 961, 255, 716, 474,798, 376, 745, 853, 694, 866, 907, 608, 486, 637, 475, 799, 812, 718,695, 867, 914, 432, 909, 487, 380, 857, 724, 698, 753, 719, 477, 915,490, 840, 814, 869, 699, 624, 382, 820, 726, 491, 815, 440, 917, 930,383, 672, 844, 727, 701, 873, 740, 498, 464, 822, 493, 931, 730, 632,444, 921, 846, 499, 823, 742, 731, 904, 852, 933, 826, 881, 847, 472,688, 446, 743, 636, 501, 962, 256, 827, 733, 746, 854, 447, 908, 963,937, 638, 476, 800, 747, 505, 855, 829, 696, 868, 910, 488, 639, 965,858, 754, 720, 478, 916, 749, 945, 870, 911, 859, 700, 755, 479, 492,816, 969, 871, 918, 384, 861, 728, 702, 874, 757, 919, 494, 932, 703,875, 922, 500, 824, 977, 495, 732, 761, 934, 882, 923, 848, 877, 744,502, 935, 828, 734, 883, 448, 925, 503, 964, 938, 993, 735, 748, 506,856, 830, 885, 939, 640, 966, 507, 831, 750, 946, 912, 967, 860, 941,889, 756, 480, 751, 509, 970, 947, 872, 862, 758, 971, 920, 949, 863,704, 876, 759, 978, 496, 973, 762, 924, 979, 953, 878, 763, 936, 884,879, 926, 504, 981, 994, 736, 765, 886, 927, 940, 995, 508, 832, 985,887, 968, 942, 997, 890, 752, 510, 948, 943, 891, 511, 972, 1001, 950,864, 893, 760, 974, 951, 980, 954, 1009, 975, 764, 955, 880, 982, 766,928, 983, 957, 996, 767, 986, 888, 998, 987, 944, 999, 892, 512, 989,1002, 894, 1003, 952, 895, 1010, 976, 1005, 956, 1011, 984, 958, 1013,768, 959, 988, 1017, 1000, 990, 991, 1004, 896, 1006, 1012, 1007, 1014,960, 1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S13: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 67, 8, 41, 130, 12, 69, 49, 514,14, 131, 20, 15, 73, 258, 22, 133, 23, 81, 36, 259, 26, 137, 97, 261,515, 38, 145, 27, 39, 265, 68, 29, 42, 161, 43, 45, 50, 70, 517, 273,193, 16, 71, 132, 74, 51, 289, 24, 75, 53, 521, 134, 82, 321, 77, 135,28, 57, 83, 138, 260, 529, 40, 98, 385, 30, 85, 139, 262, 146, 545, 31,99, 44, 89, 141, 263, 147, 101, 516, 266, 72, 46, 162, 52, 149, 47, 518,105, 267, 163, 274, 76, 54, 153, 577, 113, 269, 194, 165, 275, 78, 519,55, 136, 58, 84, 195, 290, 522, 79, 169, 277, 59, 86, 61, 523, 87, 140,100, 197, 90, 641, 291, 281, 142, 177, 91, 102, 530, 148, 143, 32, 103,264, 525, 48, 322, 293, 201, 531, 323, 150, 297, 93, 106, 546, 209, 268,386, 325, 769, 305, 164, 151, 56, 533, 107, 154, 225, 387, 329, 547,270, 114, 80, 537, 166, 109, 155, 276, 578, 60, 271, 115, 167, 549, 88,196, 62, 157, 579, 170, 278, 292, 520, 279, 198, 171, 117, 553, 178,282, 92, 642, 63, 144, 389, 294, 524, 199, 104, 337, 581, 173, 283, 202,561, 121, 179, 295, 526, 94, 152, 324, 643, 393, 298, 203, 532, 108,285, 181, 527, 210, 95, 205, 585, 299, 353, 326, 770, 185, 211, 534,401, 306, 301, 645, 110, 156, 327, 535, 116, 111, 593, 168, 213, 307,548, 330, 158, 771, 226, 118, 172, 538, 331, 227, 649, 388, 309, 217,609, 417, 338, 773, 159, 272, 550, 119, 280, 657, 333, 390, 174, 539,122, 200, 551, 180, 229, 777, 339, 313, 580, 391, 175, 541, 394, 284,554, 123, 233, 341, 673, 449, 354, 555, 395, 204, 557, 182, 296, 562,286, 582, 125, 183, 785, 206, 64, 705, 287, 300, 528, 355, 186, 583,402, 212, 644, 397, 345, 586, 207, 302, 563, 96, 801, 187, 241, 536,328, 403, 587, 214, 565, 357, 308, 646, 303, 112, 594, 160, 833, 418,332, 589, 228, 405, 647, 310, 540, 215, 120, 569, 189, 361, 595, 419,650, 409, 369, 772, 218, 552, 450, 421, 610, 311, 897, 230, 334, 542,219, 597, 176, 651, 392, 124, 774, 314, 658, 231, 340, 543, 335, 611,221, 451, 556, 425, 601, 315, 653, 234, 126, 775, 288, 659, 184, 613,342, 778, 396, 356, 584, 343, 558, 235, 674, 398, 317, 564, 346, 661,242, 559, 208, 617, 404, 358, 779, 188, 675, 237, 786, 127, 588, 304,566, 453, 665, 433, 243, 625, 347, 781, 399, 706, 216, 677, 406, 787,359, 590, 362, 567, 190, 648, 457, 570, 349, 420, 596, 407, 707, 245,802, 410, 591, 363, 681, 220, 789, 422, 571, 370, 598, 312, 573, 191,599, 411, 652, 232, 612, 249, 709, 365, 602, 465, 803, 336, 793, 423,316, 222, 654, 371, 689, 426, 603, 452, 614, 413, 660, 236, 655, 223,544, 344, 615, 373, 776, 427, 560, 481, 834, 454, 805, 318, 713, 238,835, 434, 662, 809, 348, 605, 319, 618, 455, 721, 244, 780, 429, 898,400, 837, 360, 817, 239, 676, 377, 663, 458, 568, 619, 435, 666, 350,737, 246, 899, 459, 841, 408, 782, 626, 128, 592, 364, 678, 351, 621,247, 667, 437, 788, 572, 466, 783, 412, 627, 461, 679, 600, 250, 708,366, 574, 467, 669, 424, 682, 790, 192, 804, 372, 791, 710, 441, 683,251, 629, 414, 690, 794, 367, 604, 469, 575, 656, 482, 901, 374, 806,428, 711, 616, 415, 849, 253, 685, 795, 224, 714, 375, 633, 691, 483,807, 606, 430, 664, 456, 836, 905, 473, 810, 378, 715, 620, 436, 797,693, 320, 722, 240, 607, 717, 431, 811, 865, 485, 838, 460, 697, 723,379, 913, 818, 438, 813, 622, 489, 668, 462, 839, 628, 381, 623, 680,439, 725, 819, 352, 842, 670, 248, 738, 630, 468, 684, 843, 442, 739,252, 900, 821, 463, 729, 929, 497, 850, 671, 784, 443, 631, 792, 368,845, 902, 470, 686, 634, 471, 712, 692, 416, 741, 851, 484, 825, 903,254, 687, 906, 796, 445, 635, 745, 376, 853, 961, 474, 866, 907, 716,486, 694, 808, 475, 798, 637, 432, 695, 718, 576, 380, 799, 812, 487,867, 698, 914, 255, 724, 909, 477, 857, 719, 814, 490, 608, 699, 753,440, 840, 915, 726, 491, 869, 820, 382, 815, 624, 672, 464, 930, 844,740, 383, 917, 822, 727, 498, 632, 701, 873, 444, 931, 921, 881, 493,730, 962, 933, 499, 823, 742, 846, 731, 446, 688, 904, 636, 472, 826,743, 852, 447, 847, 733, 963, 937, 476, 827, 746, 638, 501, 800, 696,854, 908, 488, 868, 855, 747, 910, 505, 829, 858, 754, 720, 256, 916,870, 700, 478, 749, 639, 816, 965, 945, 492, 755, 859, 911, 728, 479,918, 871, 874, 702, 494, 969, 861, 932, 919, 757, 500, 922, 875, 732,934, 882, 495, 824, 703, 923, 744, 502, 761, 877, 977, 848, 935, 828,384, 734, 883, 938, 964, 925, 448, 748, 735, 856, 885, 939, 993, 503,966, 830, 750, 946, 860, 831, 506, 967, 756, 941, 912, 872, 751, 507,889, 970, 947, 862, 758, 971, 920, 480, 640, 876, 863, 759, 949, 978,924, 509, 973, 762, 878, 979, 936, 704, 884, 953, 496, 763, 926, 879,981, 994, 886, 940, 927, 504, 765, 736, 887, 995, 942, 968, 985, 890,948, 832, 508, 752, 943, 997, 972, 891, 950, 1001, 974, 893, 951, 864,510, 760, 980, 954, 764, 975, 1009, 955, 880, 982, 983, 928, 996, 766,511, 957, 888, 986, 998, 987, 944, 892, 999, 767, 989, 1002, 952, 1003,894, 976, 895, 1010, 512, 956, 1005, 1011, 958, 984, 959, 988, 1013,1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960, 1015,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S14: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 37, 67, 25, 257, 21, 66, 35, 8, 130, 41, 12, 73, 133, 514,20, 49, 69, 14, 258, 15, 22, 131, 27, 81, 36, 259, 39, 137, 97, 23, 517,38, 26, 68, 265, 42, 145, 29, 70, 261, 50, 75, 161, 43, 521, 135, 71,45, 82, 273, 16, 51, 132, 193, 74, 24, 515, 138, 53, 289, 77, 134, 83,28, 98, 260, 40, 529, 57, 139, 85, 30, 146, 262, 44, 321, 545, 99, 141,266, 31, 89, 147, 263, 101, 519, 162, 72, 46, 274, 52, 149, 267, 577,47, 76, 105, 165, 194, 54, 163, 516, 385, 269, 78, 153, 55, 86, 525,290, 113, 275, 58, 79, 136, 518, 195, 84, 291, 169, 277, 87, 531, 59,140, 323, 197, 102, 641, 61, 148, 177, 281, 100, 90, 522, 293, 142, 322,201, 91, 546, 32, 143, 103, 264, 530, 48, 387, 106, 297, 209, 523, 154,93, 150, 268, 549, 164, 325, 114, 151, 579, 166, 56, 305, 107, 276, 537,270, 386, 155, 769, 80, 109, 225, 167, 533, 60, 170, 115, 196, 578, 329,271, 278, 88, 547, 157, 117, 389, 520, 337, 292, 279, 198, 642, 62, 178,171, 553, 92, 282, 202, 199, 524, 63, 144, 295, 585, 173, 393, 104, 645,121, 294, 283, 532, 353, 179, 203, 561, 324, 298, 94, 581, 108, 152,210, 526, 285, 181, 401, 770, 95, 205, 299, 527, 327, 156, 534, 306,110, 326, 643, 211, 185, 226, 539, 168, 301, 593, 116, 388, 330, 548,111, 417, 771, 213, 272, 118, 551, 307, 158, 649, 227, 172, 331, 609,338, 390, 535, 309, 217, 550, 122, 391, 538, 159, 280, 333, 580, 119,174, 777, 339, 180, 554, 200, 354, 657, 284, 313, 541, 449, 229, 582,394, 123, 182, 773, 233, 296, 562, 175, 395, 587, 64, 204, 673, 355,555, 402, 341, 647, 125, 286, 583, 183, 300, 557, 241, 212, 594, 287,345, 785, 397, 206, 528, 96, 419, 563, 186, 644, 214, 403, 705, 308,328, 586, 357, 536, 207, 187, 650, 302, 112, 565, 303, 801, 361, 228,589, 418, 160, 646, 405, 595, 310, 215, 540, 450, 332, 610, 120, 772,218, 189, 552, 230, 569, 334, 409, 651, 311, 597, 340, 421, 542, 219,658, 369, 774, 124, 231, 556, 176, 833, 392, 314, 611, 242, 653, 451,335, 778, 221, 543, 342, 601, 425, 315, 659, 184, 775, 234, 613, 356,674, 126, 288, 584, 396, 558, 235, 786, 317, 346, 564, 188, 661, 453,779, 404, 559, 343, 398, 588, 208, 617, 237, 677, 433, 706, 347, 566,362, 675, 127, 243, 897, 358, 781, 406, 590, 216, 665, 399, 567, 304,598, 359, 802, 420, 625, 457, 787, 349, 190, 570, 245, 591, 411, 648,220, 707, 312, 596, 363, 803, 465, 681, 407, 789, 422, 599, 232, 571,249, 652, 370, 835, 191, 709, 410, 614, 316, 573, 365, 660, 423, 336,222, 689, 452, 793, 371, 612, 426, 602, 236, 805, 344, 654, 413, 834,481, 713, 223, 603, 318, 544, 454, 655, 427, 615, 373, 776, 434, 560,238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429,780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 246, 568, 435, 817,458, 619, 350, 788, 466, 782, 898, 364, 667, 408, 592, 128, 621, 247,737, 437, 679, 572, 351, 682, 250, 627, 461, 708, 841, 412, 783, 366,790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791, 372,710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711, 430,575, 656, 253, 807, 415, 685, 905, 374, 616, 483, 633, 806, 224, 795,865, 428, 691, 473, 715, 836, 456, 810, 378, 606, 620, 436, 664, 722,320, 797, 431, 693, 913, 240, 607, 717, 462, 811, 485, 839, 668, 379,818, 622, 438, 838, 723, 248, 697, 381, 738, 680, 460, 813, 628, 489,900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463,739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671,792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416,825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471,576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753,724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440,820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930,446, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742,846, 921, 472, 823, 852, 933, 731, 498, 881, 636, 743, 444, 688, 904,826, 476, 754, 963, 847, 733, 501, 854, 937, 827, 447, 696, 746, 868,638, 488, 800, 908, 747, 829, 494, 858, 700, 965, 916, 478, 855, 910,720, 505, 749, 945, 859, 874, 639, 479, 755, 870, 918, 728, 500, 911,816, 871, 932, 256, 969, 861, 702, 757, 923, 492, 732, 824, 875, 977,919, 503, 934, 744, 761, 882, 495, 703, 922, 828, 877, 935, 848, 506,734, 964, 883, 938, 748, 384, 856, 925, 993, 735, 830, 966, 502, 939,885, 946, 750, 860, 756, 480, 967, 831, 889, 941, 751, 872, 507, 971,912, 758, 947, 970, 862, 978, 448, 876, 920, 640, 759, 949, 863, 762,509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926,879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948,832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510,864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511,766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894,1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000,1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992,1019, 960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S15: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 71, 273,193, 521, 529, 45, 16, 132, 74, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 30, 85, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 61, 87, 140, 100, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 48, 322, 293, 201, 323,578, 150, 297, 93, 106, 209, 549, 579, 268, 386, 325, 305, 164, 151,107, 56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155,276, 60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278,292, 279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770,144, 389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534,645, 535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210,538, 95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110,156, 327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158,226, 118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580,119, 541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391,64, 394, 284, 175, 233, 341, 449, 354, 395, 204, 123, 673, 555, 557,562, 582, 296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644,586, 563, 300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187,241, 536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589,647, 112, 540, 569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189,552, 610, 897, 160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597,651, 774, 658, 311, 120, 334, 219, 543, 611, 176, 392, 231, 314, 124,340, 335, 221, 451, 425, 315, 556, 601, 653, 234, 775, 659, 613, 235,288, 453, 126, 342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559,617, 779, 675, 184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188,588, 566, 665, 625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787,590, 567, 648, 406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465,802, 420, 407, 245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422,599, 652, 612, 709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411,232, 249, 365, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413,481, 236, 223, 344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560,834, 805, 713, 835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455,837, 817, 676, 663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568,619, 666, 737, 899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667,788, 572, 783, 627, 679, 408, 364, 351, 192, 247, 437, 466, 412, 461,250, 366, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 441,690, 794, 604, 575, 467, 424, 372, 251, 414, 367, 469, 482, 374, 656,901, 806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807,606, 483, 473, 224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 485,430, 456, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 378, 436,813, 320, 622, 240, 431, 460, 379, 668, 839, 489, 438, 628, 623, 462,381, 439, 352, 497, 680, 725, 819, 842, 670, 738, 630, 468, 248, 442,463, 470, 443, 252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784,631, 792, 845, 902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903,687, 471, 416, 484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961,866, 907, 716, 694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812,867, 432, 380, 698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490,699, 753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493,464, 672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881,730, 383, 499, 444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688,904, 636, 826, 743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501,488, 638, 505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754,720, 916, 870, 478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492,479, 728, 918, 871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932,919, 757, 922, 875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877,848, 935, 828, 734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856,885, 939, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912,872, 751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863,759, 949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763,504, 926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968,985, 508, 890, 948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974,893, 951, 864, 760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983,928, 996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989,1002, 952, 1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959,988, 1013, 1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896,960, 1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S16: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 25, 21, 35, 257, 66, 37, 8, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 73, 258, 15, 22, 131, 81, 27, 36, 259, 137, 39, 97, 23, 517,38, 26, 68, 265, 42, 145, 29, 70, 261, 50, 43, 161, 71, 521, 45, 75, 82,132, 273, 193, 16, 51, 74, 53, 24, 515, 135, 138, 289, 77, 134, 83, 28,98, 260, 40, 529, 57, 139, 85, 30, 146, 262, 44, 321, 545, 99, 141, 266,31, 89, 147, 263, 72, 519, 162, 46, 101, 385, 149, 52, 47, 577, 76, 267,54, 274, 165, 194, 105, 516, 163, 269, 78, 153, 275, 55, 525, 58, 113,136, 86, 79, 290, 518, 195, 84, 291, 59, 277, 169, 531, 100, 140, 323,197, 87, 641, 177, 61, 90, 281, 102, 148, 522, 293, 142, 322, 91, 143,546, 32, 201, 103, 264, 530, 106, 387, 48, 297, 523, 209, 154, 93, 150,268, 164, 537, 769, 533, 325, 151, 56, 166, 107, 305, 114, 578, 276,549, 270, 386, 155, 80, 109, 225, 167, 60, 579, 170, 115, 196, 329, 271,278, 157, 547, 88, 117, 389, 520, 337, 292, 279, 198, 642, 62, 178, 171,553, 92, 282, 199, 63, 524, 144, 173, 295, 585, 202, 393, 104, 645, 121,294, 283, 532, 353, 179, 203, 561, 324, 298, 94, 581, 152, 210, 181,526, 285, 108, 401, 770, 95, 205, 299, 527, 327, 156, 534, 306, 110,326, 643, 211, 116, 185, 539, 168, 301, 593, 226, 388, 330, 548, 111,417, 771, 158, 272, 213, 551, 307, 118, 649, 172, 227, 331, 609, 338,390, 535, 309, 217, 550, 159, 391, 538, 119, 280, 333, 580, 174, 122,777, 339, 200, 554, 180, 657, 354, 284, 541, 313, 449, 582, 229, 394,773, 123, 175, 673, 555, 785, 204, 562, 395, 182, 341, 583, 557, 64,296, 286, 233, 125, 183, 206, 287, 300, 355, 212, 402, 186, 397, 587,345, 594, 647, 528, 96, 563, 241, 644, 207, 705, 328, 586, 403, 536,214, 357, 308, 419, 565, 801, 589, 187, 302, 646, 112, 569, 303, 595,361, 228, 650, 772, 418, 540, 215, 405, 310, 189, 450, 332, 218, 610,597, 552, 651, 160, 230, 120, 334, 409, 311, 421, 219, 542, 369, 658,231, 774, 392, 176, 556, 314, 833, 340, 221, 611, 653, 335, 451, 778,124, 543, 342, 601, 425, 234, 659, 235, 775, 315, 613, 126, 674, 356,184, 584, 288, 558, 396, 564, 661, 242, 779, 559, 317, 346, 617, 675,897, 404, 343, 398, 188, 453, 208, 433, 786, 237, 588, 566, 665, 781,347, 362, 127, 243, 358, 706, 406, 677, 590, 216, 399, 567, 304, 598,359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220, 648, 312,707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191, 571, 410,652, 370, 835, 411, 709, 232, 614, 316, 573, 365, 660, 423, 336, 222,689, 452, 793, 371, 612, 426, 602, 236, 805, 413, 654, 481, 834, 223,713, 344, 603, 318, 544, 454, 655, 427, 615, 373, 776, 434, 560, 238,899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662, 429, 780,239, 676, 360, 837, 400, 626, 246, 663, 678, 435, 568, 458, 817, 350,619, 459, 788, 466, 782, 898, 364, 667, 408, 592, 128, 621, 437, 737,351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783, 366, 790,441, 600, 424, 669, 629, 467, 901, 251, 849, 804, 372, 791, 192, 710,482, 574, 690, 414, 683, 367, 604, 794, 469, 714, 374, 711, 253, 575,656, 483, 807, 415, 685, 905, 375, 616, 224, 633, 806, 428, 795, 865,430, 691, 473, 715, 836, 456, 810, 378, 606, 620, 436, 664, 722, 485,797, 320, 693, 913, 431, 607, 717, 240, 811, 379, 839, 668, 438, 818,622, 460, 838, 723, 248, 697, 381, 738, 680, 462, 813, 628, 489, 900,842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670, 463, 739,684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368, 671, 792,443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796, 416, 825,961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907, 471, 576,716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487, 753, 724,799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915, 440, 820,840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740, 930, 672,917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742, 846, 921,472, 823, 852, 731, 498, 881, 743, 444, 904, 826, 501, 688, 446, 933,847, 636, 963, 733, 937, 476, 854, 827, 447, 746, 868, 638, 908, 800,488, 696, 747, 829, 858, 754, 855, 916, 965, 478, 910, 720, 505, 749,945, 639, 755, 870, 256, 911, 700, 859, 479, 918, 871, 728, 494, 874,969, 932, 702, 816, 861, 500, 757, 492, 875, 732, 923, 824, 977, 919,934, 744, 761, 882, 495, 703, 922, 877, 935, 828, 848, 734, 503, 883,938, 384, 964, 748, 506, 856, 925, 993, 735, 502, 830, 966, 939, 885,946, 750, 860, 756, 480, 967, 831, 889, 941, 751, 872, 507, 971, 912,758, 947, 970, 862, 978, 448, 876, 920, 640, 759, 949, 863, 762, 509,973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994, 926, 879,981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890, 948, 832,508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954, 510, 864,982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928, 511, 766,957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005, 894, 1011,958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959, 1000, 1006,990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896, 1014, 992, 1019,960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S17: [1, 2, 5, 9, 3, 17, 33, 7, 65, 513, 4, 13, 6, 19, 129, 10,34, 18, 11, 257, 21, 35, 25, 66, 37, 8, 67, 130, 12, 41, 20, 133, 514,14, 69, 49, 15, 73, 258, 22, 131, 27, 36, 81, 259, 137, 39, 23, 261,517, 38, 26, 97, 68, 265, 42, 145, 29, 161, 70, 50, 75, 43, 521, 273,193, 71, 45, 132, 82, 16, 289, 51, 135, 74, 515, 24, 134, 321, 53, 77,83, 138, 57, 28, 260, 529, 98, 40, 385, 139, 85, 30, 262, 146, 545, 44,99, 141, 31, 89, 263, 147, 72, 519, 266, 162, 46, 101, 149, 52, 47, 577,76, 267, 105, 274, 165, 194, 54, 516, 163, 269, 78, 153, 275, 55, 525,84, 58, 113, 86, 136, 290, 518, 195, 79, 291, 59, 277, 169, 531, 100,140, 197, 87, 177, 641, 61, 90, 281, 102, 148, 293, 522, 142, 322, 143,91, 201, 546, 32, 103, 264, 106, 530, 323, 150, 297, 48, 523, 93, 164,268, 386, 325, 305, 537, 769, 533, 209, 154, 151, 107, 56, 166, 387,578, 329, 549, 270, 114, 155, 80, 225, 167, 276, 109, 579, 271, 60, 115,196, 170, 157, 88, 547, 62, 278, 292, 520, 279, 117, 198, 178, 642, 171,282, 92, 553, 202, 199, 389, 294, 524, 63, 144, 337, 585, 173, 283, 121,645, 104, 179, 295, 532, 203, 94, 324, 561, 393, 298, 152, 581, 210,285, 181, 526, 108, 95, 205, 770, 299, 353, 326, 527, 211, 185, 534,401, 306, 301, 643, 156, 110, 327, 539, 116, 168, 593, 158, 111, 307,548, 330, 213, 771, 226, 118, 172, 551, 331, 227, 649, 388, 309, 159,609, 417, 338, 535, 217, 272, 550, 119, 280, 538, 333, 390, 174, 580,122, 180, 777, 200, 229, 554, 339, 657, 313, 541, 391, 123, 582, 394,284, 773, 233, 673, 555, 785, 175, 341, 705, 449, 562, 354, 801, 395,204, 182, 528, 583, 557, 296, 286, 64, 125, 206, 241, 644, 586, 563,287, 300, 355, 183, 402, 212, 397, 345, 587, 833, 565, 96, 186, 207,328, 646, 536, 403, 214, 594, 357, 308, 419, 187, 589, 569, 302, 647,228, 303, 897, 595, 361, 112, 650, 772, 418, 540, 215, 405, 310, 189,450, 332, 160, 218, 610, 597, 552, 651, 230, 120, 334, 409, 542, 774,611, 658, 311, 421, 601, 219, 369, 176, 653, 392, 231, 314, 340, 543,335, 234, 556, 775, 124, 315, 659, 613, 342, 778, 451, 221, 425, 356,674, 584, 126, 235, 184, 396, 242, 558, 661, 617, 317, 343, 346, 779,564, 404, 288, 398, 453, 675, 559, 786, 433, 188, 358, 208, 665, 588,781, 706, 677, 237, 347, 566, 362, 127, 243, 590, 406, 216, 399, 567,304, 598, 359, 802, 420, 625, 457, 787, 349, 245, 570, 190, 591, 220,648, 312, 707, 363, 596, 465, 803, 407, 681, 422, 789, 249, 599, 191,571, 370, 652, 410, 835, 411, 709, 481, 614, 232, 573, 316, 660, 365,423, 336, 689, 371, 793, 222, 612, 452, 602, 426, 805, 413, 654, 454,834, 318, 713, 236, 603, 344, 544, 373, 655, 223, 615, 427, 776, 434,560, 238, 899, 618, 348, 809, 244, 721, 455, 666, 319, 605, 377, 662,429, 780, 239, 676, 360, 837, 459, 626, 400, 663, 678, 435, 568, 458,817, 350, 619, 128, 788, 246, 782, 898, 437, 667, 466, 592, 408, 621,364, 737, 351, 679, 572, 247, 682, 250, 627, 461, 708, 841, 412, 783,366, 790, 441, 600, 375, 669, 629, 424, 901, 467, 849, 804, 251, 791,372, 710, 192, 574, 690, 482, 683, 414, 604, 794, 367, 714, 469, 711,374, 575, 656, 428, 807, 415, 685, 905, 253, 616, 483, 633, 806, 430,795, 865, 224, 691, 456, 715, 836, 473, 810, 378, 606, 620, 436, 664,722, 320, 797, 485, 693, 913, 431, 607, 717, 489, 811, 460, 839, 668,240, 818, 622, 379, 838, 723, 438, 697, 462, 738, 680, 381, 813, 628,248, 900, 842, 442, 623, 929, 352, 725, 784, 470, 630, 819, 439, 670,463, 739, 684, 252, 843, 850, 497, 902, 821, 729, 468, 634, 903, 368,671, 792, 443, 845, 631, 475, 686, 851, 484, 692, 712, 380, 866, 796,416, 825, 961, 741, 254, 906, 635, 445, 694, 745, 486, 808, 687, 907,471, 576, 716, 376, 867, 914, 474, 853, 637, 798, 432, 695, 812, 487,753, 724, 799, 490, 857, 909, 255, 718, 608, 931, 477, 698, 726, 915,440, 820, 840, 869, 493, 719, 699, 382, 814, 624, 815, 499, 873, 740,930, 672, 917, 822, 464, 727, 962, 844, 491, 632, 730, 701, 383, 742,846, 921, 472, 823, 852, 731, 498, 881, 743, 444, 904, 688, 826, 501,933, 847, 446, 636, 746, 827, 733, 447, 963, 937, 476, 854, 868, 638,908, 488, 696, 747, 829, 754, 855, 858, 916, 965, 478, 910, 720, 800,700, 494, 505, 749, 945, 859, 639, 755, 256, 969, 479, 384, 870, 492,911, 816, 918, 728, 871, 874, 702, 932, 861, 500, 757, 732, 824, 923,875, 977, 919, 503, 934, 744, 761, 882, 495, 703, 922, 848, 993, 448,502, 877, 734, 828, 883, 935, 964, 506, 938, 748, 856, 925, 735, 830,966, 939, 885, 507, 750, 946, 860, 756, 480, 967, 831, 889, 941, 751,872, 971, 912, 758, 947, 970, 862, 978, 876, 920, 640, 759, 949, 863,762, 509, 973, 924, 878, 953, 887, 936, 979, 763, 504, 884, 704, 994,926, 879, 981, 942, 765, 496, 927, 886, 995, 736, 940, 985, 968, 890,948, 832, 508, 943, 752, 974, 997, 891, 950, 760, 893, 972, 1001, 954,510, 864, 982, 951, 975, 764, 1009, 980, 880, 955, 987, 996, 892, 928,511, 766, 957, 998, 983, 888, 986, 944, 999, 1002, 767, 989, 952, 1005,894, 1011, 958, 976, 512, 1003, 895, 984, 1010, 956, 988, 1013, 959,1000, 1006, 990, 1017, 991, 1012, 768, 1004, 1015, 1007, 1018, 896,1014, 992, 1019, 960, 1021, 1016, 1008, 1020, 1022, 1023, 1024];

sequence S18: [1, 2, 3, 5, 9, 17, 33, 4, 6, 65, 7, 10, 11, 129, 18, 13,19, 34, 257, 21, 35, 25, 66, 37, 67, 513, 8, 12, 130, 41, 69, 14, 20,131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261, 97,145, 27, 514, 39, 515, 265, 68, 42, 29, 161, 70, 43, 517, 50, 71, 273,45, 521, 529, 16, 132, 74, 193, 51, 289, 545, 24, 75, 53, 134, 82, 321,77, 135, 28, 57, 83, 138, 260, 40, 98, 385, 85, 30, 139, 262, 146, 31,99, 516, 44, 89, 141, 263, 147, 101, 266, 72, 46, 162, 518, 577, 519,52, 149, 522, 47, 76, 267, 163, 274, 523, 641, 105, 54, 153, 78, 269,194, 165, 275, 55, 84, 530, 525, 531, 136, 58, 113, 195, 290, 79, 169,277, 59, 86, 100, 87, 140, 61, 197, 90, 291, 281, 546, 769, 142, 177,91, 102, 148, 143, 533, 547, 537, 32, 103, 264, 106, 322, 293, 201, 323,578, 150, 297, 48, 93, 209, 549, 579, 268, 386, 325, 305, 164, 151, 107,56, 154, 225, 387, 329, 270, 114, 520, 553, 642, 80, 166, 109, 155, 276,60, 271, 115, 167, 524, 581, 561, 157, 196, 170, 198, 171, 278, 292,279, 117, 88, 62, 178, 282, 526, 643, 532, 527, 63, 92, 585, 770, 144,389, 294, 199, 104, 337, 173, 283, 202, 121, 179, 295, 94, 534, 645,535, 593, 548, 771, 152, 324, 393, 298, 203, 108, 285, 181, 210, 538,95, 205, 299, 353, 649, 609, 326, 185, 211, 401, 306, 301, 110, 156,327, 116, 111, 773, 550, 657, 539, 551, 168, 213, 307, 330, 158, 226,118, 172, 331, 227, 388, 309, 217, 417, 338, 159, 777, 272, 580, 119,541, 554, 280, 333, 390, 174, 122, 200, 180, 229, 339, 313, 391, 64,394, 284, 175, 123, 341, 449, 354, 395, 233, 204, 673, 555, 557, 562,582, 296, 286, 182, 206, 125, 785, 705, 183, 287, 528, 583, 644, 586,563, 300, 355, 212, 402, 186, 397, 345, 207, 302, 801, 96, 187, 241,536, 587, 565, 646, 594, 328, 403, 214, 357, 308, 303, 833, 589, 647,112, 540, 569, 595, 650, 772, 228, 418, 332, 215, 405, 310, 189, 552,610, 897, 160, 218, 361, 419, 409, 369, 230, 450, 421, 542, 597, 651,774, 658, 311, 120, 334, 219, 543, 611, 231, 392, 234, 314, 176, 340,335, 221, 451, 425, 315, 556, 601, 653, 124, 775, 659, 613, 235, 288,453, 126, 342, 396, 778, 584, 558, 674, 356, 343, 564, 661, 559, 617,779, 675, 184, 398, 433, 317, 346, 242, 208, 404, 358, 786, 188, 588,566, 665, 625, 781, 237, 127, 243, 347, 399, 706, 216, 677, 787, 590,567, 648, 406, 359, 304, 570, 596, 362, 707, 190, 457, 349, 465, 802,420, 407, 245, 410, 591, 681, 789, 571, 598, 363, 573, 220, 422, 599,652, 612, 709, 602, 803, 370, 793, 312, 191, 654, 689, 603, 411, 232,249, 365, 336, 423, 614, 660, 655, 316, 222, 371, 426, 452, 413, 481,236, 223, 344, 318, 544, 373, 615, 427, 776, 128, 454, 238, 560, 834,805, 713, 835, 662, 809, 605, 618, 721, 780, 434, 898, 319, 455, 837,817, 676, 663, 348, 429, 400, 377, 244, 239, 458, 435, 360, 568, 619,666, 737, 899, 841, 782, 626, 350, 246, 459, 592, 678, 621, 667, 788,572, 783, 627, 679, 408, 364, 351, 192, 247, 437, 466, 412, 461, 250,366, 600, 708, 574, 669, 682, 790, 804, 791, 710, 683, 629, 441, 690,794, 604, 575, 467, 424, 372, 251, 482, 414, 469, 367, 374, 656, 901,806, 711, 428, 415, 253, 616, 849, 685, 795, 714, 633, 691, 807, 606,483, 473, 224, 664, 836, 905, 810, 715, 620, 797, 693, 375, 485, 430,456, 722, 607, 717, 811, 865, 838, 697, 723, 913, 818, 378, 436, 813,320, 622, 240, 431, 460, 379, 668, 839, 489, 438, 628, 623, 462, 381,439, 352, 497, 680, 725, 819, 842, 670, 738, 630, 468, 248, 442, 463,470, 443, 252, 684, 843, 739, 900, 821, 729, 929, 850, 671, 784, 631,792, 845, 902, 686, 368, 634, 712, 254, 692, 741, 851, 825, 903, 687,471, 416, 484, 445, 376, 474, 906, 796, 486, 635, 745, 853, 961, 866,907, 716, 694, 808, 475, 798, 637, 695, 255, 718, 576, 799, 812, 867,432, 380, 698, 914, 487, 724, 909, 857, 719, 477, 814, 608, 490, 699,753, 840, 915, 726, 869, 820, 815, 440, 491, 624, 382, 498, 493, 464,672, 930, 844, 740, 917, 822, 727, 632, 701, 873, 931, 921, 881, 730,383, 499, 444, 446, 472, 962, 933, 823, 742, 846, 731, 447, 688, 904,636, 826, 743, 852, 847, 256, 476, 733, 963, 937, 827, 746, 501, 488,638, 505, 800, 696, 854, 908, 868, 855, 747, 910, 829, 858, 754, 720,916, 870, 478, 700, 749, 639, 816, 965, 945, 755, 859, 911, 492, 479,728, 918, 871, 384, 494, 500, 874, 702, 969, 495, 861, 502, 932, 919,757, 922, 875, 732, 977, 934, 882, 761, 824, 703, 923, 744, 877, 848,935, 828, 734, 883, 448, 938, 503, 964, 925, 993, 748, 735, 856, 885,939, 506, 966, 507, 830, 750, 946, 860, 831, 967, 756, 941, 912, 872,751, 889, 480, 970, 947, 862, 758, 971, 509, 920, 640, 876, 863, 759,949, 978, 924, 973, 762, 878, 979, 496, 936, 704, 884, 953, 763, 504,926, 879, 981, 994, 886, 940, 927, 765, 736, 887, 995, 942, 968, 985,508, 890, 948, 832, 752, 943, 997, 972, 891, 1001, 510, 950, 974, 893,951, 864, 760, 1009, 511, 980, 954, 764, 975, 955, 880, 982, 983, 928,996, 766, 957, 888, 986, 998, 987, 944, 892, 999, 767, 512, 989, 1002,952, 1003, 894, 976, 895, 1010, 956, 1005, 1011, 958, 984, 959, 988,1013, 1000, 1017, 768, 990, 1004, 991, 1006, 1012, 1007, 1014, 896, 960,1015, 1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024];

sequence S19: [1, 2, 3, 5, 9, 17, 33, 4, 257, 513, 6, 65, 7, 10, 11,129, 18, 13, 19, 34, 21, 35, 25, 66, 37, 258, 8, 130, 67, 12, 41, 69,514, 20, 14, 131, 49, 15, 73, 259, 22, 133, 36, 23, 81, 26, 137, 38, 27,515, 261, 97, 39, 68, 42, 145, 29, 70, 43, 265, 50, 161, 71, 517, 45,193, 132, 273, 74, 51, 134, 82, 75, 16, 289, 521, 24, 53, 135, 77, 57,83, 260, 28, 138, 98, 529, 40, 262, 85, 139, 30, 146, 44, 321, 545, 99,89, 141, 31, 263, 147, 46, 72, 516, 101, 266, 162, 52, 149, 47, 267,769, 76, 105, 163, 385, 54, 153, 78, 518, 194, 274, 165, 55, 84, 269,577, 136, 58, 113, 275, 79, 195, 519, 59, 290, 169, 86, 140, 277, 522,100, 87, 291, 197, 142, 523, 61, 281, 90, 102, 322, 148, 641, 177, 91,293, 143, 201, 530, 264, 32, 150, 386, 525, 103, 106, 93, 323, 48, 531,164, 268, 151, 209, 546, 297, 107, 154, 325, 533, 166, 56, 276, 114,155, 547, 270, 80, 109, 537, 387, 225, 167, 305, 578, 60, 115, 271, 196,549, 329, 170, 157, 278, 770, 88, 171, 389, 520, 117, 292, 198, 62, 642,279, 178, 92, 579, 337, 199, 282, 144, 524, 63, 393, 121, 553, 294, 202,283, 581, 173, 104, 353, 532, 179, 295, 94, 526, 203, 324, 181, 643,298, 108, 401, 561, 152, 210, 285, 527, 95, 326, 205, 585, 299, 156,771, 306, 211, 110, 534, 417, 168, 327, 645, 185, 301, 548, 116, 449,226, 535, 388, 158, 593, 330, 111, 307, 538, 213, 118, 649, 390, 172,338, 550, 227, 331, 539, 217, 272, 773, 159, 280, 609, 119, 309, 174,551, 391, 122, 580, 333, 200, 554, 180, 229, 657, 313, 175, 541, 339,123, 582, 284, 204, 394, 555, 64, 354, 777, 182, 296, 562, 233, 341,673, 395, 583, 125, 286, 557, 206, 402, 705, 183, 300, 644, 212, 355,785, 186, 345, 586, 241, 397, 563, 207, 287, 646, 96, 594, 403, 302,587, 214, 328, 528, 187, 801, 357, 112, 536, 418, 228, 565, 308, 647,405, 215, 589, 303, 189, 569, 332, 595, 218, 361, 772, 419, 230, 540,310, 650, 160, 409, 610, 334, 552, 120, 450, 774, 219, 597, 421, 231,651, 311, 542, 340, 658, 234, 392, 556, 314, 833, 176, 369, 611, 124,601, 335, 451, 653, 221, 543, 315, 775, 184, 425, 659, 342, 558, 235,584, 396, 613, 356, 126, 778, 343, 674, 453, 564, 242, 398, 661, 208,559, 317, 779, 346, 588, 188, 358, 617, 404, 675, 237, 897, 433, 566,347, 665, 127, 590, 399, 457, 706, 243, 786, 288, 677, 406, 567, 190,596, 359, 781, 362, 648, 216, 570, 349, 625, 304, 245, 787, 420, 591,407, 707, 465, 571, 220, 802, 363, 681, 410, 598, 191, 652, 422, 789,312, 612, 249, 599, 370, 803, 411, 709, 336, 654, 232, 573, 365, 793,481, 222, 423, 602, 316, 614, 371, 834, 236, 660, 452, 689, 426, 603,413, 805, 223, 655, 344, 713, 427, 776, 238, 544, 373, 662, 454, 898,318, 615, 244, 618, 605, 434, 835, 348, 560, 455, 676, 239, 780, 400,663, 319, 721, 377, 809, 458, 619, 128, 666, 429, 837, 678, 360, 568,435, 788, 246, 626, 350, 667, 459, 782, 592, 437, 621, 247, 899, 364,737, 408, 679, 466, 817, 572, 351, 627, 250, 783, 461, 708, 841, 412,682, 467, 669, 366, 790, 192, 600, 683, 424, 901, 441, 629, 804, 372,710, 482, 574, 251, 791, 690, 414, 604, 367, 849, 711, 469, 794, 374,656, 428, 575, 905, 253, 633, 483, 806, 714, 473, 795, 415, 685, 616,375, 865, 691, 224, 807, 430, 606, 715, 378, 836, 456, 693, 810, 436,620, 913, 485, 664, 431, 722, 797, 240, 607, 838, 379, 717, 460, 811,668, 320, 818, 723, 438, 622, 929, 489, 680, 381, 839, 697, 248, 813,628, 462, 961, 738, 439, 900, 670, 468, 842, 623, 442, 819, 725, 497,630, 463, 902, 684, 252, 850, 739, 352, 843, 729, 784, 470, 671, 792,443, 631, 821, 368, 686, 903, 484, 634, 845, 471, 712, 692, 445, 741,825, 474, 687, 851, 635, 254, 796, 716, 486, 906, 576, 416, 866, 694,808, 376, 745, 853, 475, 907, 637, 487, 798, 718, 914, 490, 695, 812,432, 724, 867, 698, 380, 857, 753, 477, 909, 719, 799, 255, 608, 915,814, 440, 726, 840, 699, 491, 869, 624, 382, 930, 740, 820, 498, 917,727, 815, 464, 701, 844, 730, 444, 873, 931, 742, 493, 822, 672, 921,383, 846, 632, 962, 499, 731, 933, 743, 823, 446, 852, 746, 904, 472,826, 688, 881, 501, 636, 847, 963, 733, 256, 827, 696, 937, 476, 854,747, 908, 868, 447, 638, 855, 965, 754, 505, 910, 720, 829, 858, 488,700, 870, 916, 478, 749, 945, 859, 639, 911, 492, 969, 755, 800, 918,479, 702, 871, 874, 728, 494, 861, 816, 757, 932, 919, 500, 977, 732,875, 922, 703, 495, 934, 824, 761, 882, 384, 923, 848, 744, 877, 993,734, 502, 935, 828, 883, 748, 964, 503, 938, 925, 735, 856, 939, 750,506, 885, 966, 830, 756, 946, 860, 448, 967, 751, 912, 831, 889, 970,507, 640, 941, 872, 947, 758, 862, 971, 509, 949, 759, 876, 920, 978,863, 762, 480, 973, 924, 979, 878, 704, 936, 953, 884, 496, 994, 763,926, 879, 981, 886, 940, 765, 504, 995, 985, 927, 887, 736, 942, 890,968, 948, 997, 508, 943, 752, 891, 972, 832, 950, 1001, 893, 760, 974,951, 510, 980, 954, 1009, 975, 764, 864, 982, 955, 880, 996, 983, 957,986, 511, 766, 998, 928, 888, 987, 999, 1002, 944, 892, 989, 767, 952,1003, 894, 1010, 976, 956, 512, 1005, 895, 1011, 958, 984, 1013, 768,988, 959, 1017, 1000, 990, 1004, 991, 1006, 1012, 1007, 896, 1014, 1015,1018, 960, 1019, 1021, 992, 1008, 1016, 1020, 1022, 1023, 1024]; and

sequence S20: [1, 2, 3, 5, 9, 17, 33, 4, 6, 513, 65, 7, 10, 11, 129, 18,13, 19, 34, 257, 21, 35, 25, 66, 37, 67, 8, 12, 130, 41, 69, 14, 514,20, 131, 49, 15, 73, 258, 22, 133, 36, 81, 23, 259, 26, 137, 38, 261,515, 97, 145, 27, 39, 265, 68, 42, 29, 161, 70, 43, 50, 75, 517, 273,193, 71, 45, 132, 16, 74, 289, 51, 24, 53, 521, 134, 82, 321, 77, 135,28, 57, 83, 138, 260, 529, 40, 98, 385, 30, 85, 139, 262, 146, 545, 31,99, 44, 89, 141, 263, 147, 72, 516, 266, 46, 101, 162, 52, 149, 47, 518,76, 267, 163, 274, 105, 54, 153, 577, 78, 269, 194, 165, 275, 55, 519,84, 136, 58, 113, 195, 290, 522, 79, 169, 277, 59, 86, 61, 523, 87, 140,100, 197, 90, 641, 291, 281, 142, 177, 91, 102, 530, 148, 143, 32, 103,264, 525, 106, 322, 293, 201, 531, 323, 150, 297, 48, 93, 546, 209, 268,386, 325, 769, 305, 164, 151, 107, 533, 56, 154, 225, 387, 329, 547,270, 114, 80, 537, 166, 109, 155, 276, 578, 60, 271, 115, 167, 549, 157,196, 170, 198, 579, 171, 278, 292, 520, 279, 117, 88, 62, 524, 178, 282,63, 642, 92, 144, 389, 294, 553, 199, 104, 337, 581, 173, 283, 202, 526,121, 179, 295, 532, 94, 152, 324, 643, 393, 298, 203, 561, 108, 285,181, 527, 210, 95, 205, 585, 299, 353, 326, 770, 185, 211, 534, 401,306, 301, 645, 110, 156, 327, 548, 116, 111, 593, 168, 213, 307, 535,330, 158, 771, 226, 118, 172, 538, 331, 227, 649, 388, 309, 217, 550,417, 338, 773, 159, 272, 609, 119, 280, 657, 333, 390, 174, 539, 122,200, 551, 180, 229, 777, 339, 313, 580, 391, 123, 554, 394, 284, 541,64, 175, 341, 673, 449, 354, 582, 395, 233, 555, 204, 296, 562, 286,587, 182, 206, 785, 125, 183, 705, 287, 300, 583, 355, 212, 557, 402,186, 644, 397, 345, 528, 207, 302, 586, 96, 801, 187, 241, 563, 328,403, 536, 214, 565, 357, 308, 646, 303, 112, 594, 228, 833, 418, 332,589, 215, 405, 647, 310, 540, 189, 160, 569, 218, 361, 595, 419, 650,409, 369, 772, 230, 552, 450, 421, 610, 311, 897, 120, 334, 542, 219,597, 176, 651, 392, 231, 774, 314, 658, 124, 340, 543, 335, 611, 221,451, 556, 425, 601, 315, 653, 234, 235, 775, 288, 659, 453, 584, 126,778, 342, 396, 558, 356, 613, 343, 674, 184, 398, 564, 433, 661, 317,559, 346, 588, 242, 208, 779, 404, 675, 358, 786, 188, 617, 237, 566,127, 665, 243, 347, 590, 399, 781, 216, 706, 406, 677, 359, 787, 304,567, 362, 596, 190, 648, 457, 570, 349, 465, 625, 420, 707, 407, 802,245, 591, 410, 681, 363, 789, 220, 571, 422, 598, 370, 573, 312, 599,191, 652, 411, 612, 232, 709, 249, 602, 365, 803, 336, 793, 423, 316,222, 654, 371, 689, 426, 603, 452, 614, 413, 660, 481, 655, 236, 544,223, 615, 344, 776, 318, 618, 373, 834, 427, 805, 128, 713, 454, 835,238, 662, 809, 434, 560, 319, 605, 455, 721, 348, 780, 429, 898, 400,837, 377, 817, 244, 676, 239, 663, 458, 619, 568, 435, 666, 360, 737,350, 899, 246, 841, 459, 782, 626, 408, 592, 364, 678, 351, 621, 437,667, 192, 788, 572, 247, 783, 466, 627, 412, 679, 669, 461, 708, 250,682, 366, 710, 441, 683, 790, 467, 804, 424, 791, 629, 372, 600, 251,574, 414, 690, 794, 367, 575, 469, 604, 656, 482, 901, 374, 806, 428,711, 616, 415, 849, 253, 685, 795, 483, 714, 473, 633, 691, 224, 807,606, 375, 664, 485, 836, 905, 430, 810, 456, 715, 620, 378, 797, 693,436, 722, 320, 607, 717, 240, 811, 865, 431, 838, 460, 697, 723, 379,913, 818, 489, 813, 622, 438, 668, 462, 839, 628, 381, 623, 680, 439,725, 819, 352, 842, 670, 497, 738, 630, 468, 684, 843, 248, 739, 442,900, 821, 463, 729, 929, 470, 850, 671, 784, 443, 631, 792, 252, 845,902, 368, 686, 634, 254, 712, 692, 471, 741, 851, 416, 825, 903, 484,635, 906, 796, 445, 576, 687, 376, 853, 961, 474, 866, 907, 745, 486,716, 808, 475, 798, 694, 255, 718, 637, 695, 432, 799, 812, 380, 867,724, 914, 487, 698, 909, 477, 857, 719, 814, 490, 608, 699, 753, 440,840, 915, 726, 491, 869, 820, 382, 815, 624, 740, 498, 930, 844, 727,493, 917, 822, 701, 464, 672, 730, 873, 383, 931, 921, 881, 499, 742,962, 933, 444, 823, 632, 846, 731, 446, 688, 904, 743, 472, 826, 636,852, 447, 847, 733, 963, 937, 256, 827, 746, 747, 476, 800, 965, 638,854, 501, 908, 868, 855, 696, 488, 910, 945, 829, 858, 505, 754, 720,916, 478, 870, 700, 749, 639, 755, 492, 859, 911, 728, 918, 479, 871,816, 874, 702, 384, 969, 861, 977, 932, 919, 494, 757, 922, 875, 732,934, 500, 882, 824, 703, 923, 495, 744, 761, 877, 848, 935, 828, 502,734, 883, 938, 964, 925, 448, 993, 748, 735, 856, 830, 885, 503, 939,640, 966, 750, 946, 831, 506, 967, 860, 941, 912, 889, 756, 507, 751,970, 947, 872, 862, 758, 971, 480, 920, 876, 863, 949, 704, 759, 978,509, 924, 973, 762, 878, 953, 979, 936, 884, 496, 763, 926, 879, 981,994, 886, 940, 927, 504, 765, 995, 985, 736, 887, 997, 942, 968, 890,948, 508, 832, 752, 943, 972, 891, 1001, 950, 974, 893, 951, 864, 510,1009, 980, 760, 954, 975, 982, 955, 764, 880, 766, 983, 928, 996, 511,957, 888, 986, 998, 987, 767, 944, 892, 999, 989, 1002, 952, 1003, 894,1010, 1005, 976, 512, 895, 1011, 956, 958, 984, 959, 768, 988, 1013,1000, 1017, 990, 1004, 991, 896, 1006, 1012, 1007, 1014, 960, 1015,1018, 1019, 992, 1021, 1008, 1016, 1020, 1022, 1023, 1024].

The foregoing sequences with relatively good performance that areobtained through simulation may be compared by using a presetperformance determining rule. Optionally, this embodiment of thisapplication provides an example of a performance determining rule, butthis is not limited thereto.

A possible performance determining rule is described as follows.

Evaluation measurement: signal-to-noise ratios (SNR) required when ablock error rate (BLER) reaches 10⁻² and 10⁻³.

Simulation Assumption:

Channel Additive white Gaussian noise (AWGN) channel Modulation modeQuadrature phase shift keying (QPSK) Information code K = [8,min(200,K_(max,N))], where block length K (K K_(max,N) = └5N/6 − (J +J′)┘ does not include K = min(200,K_(max,N)), K_(max,N)], where a CRCbit) K_(max,N) = └5N/6 − (J + J′)┘ A K value that enables a bit rate tobe less than 1/8 is not considered. Code length N {64, 128, 256, 512,1024} Decoding algorithm LLR-based min-sum decoding algorithm for alist-X Size of a list X 1, 2, 4, 8, and 16 (CRC check is performed byusing only eight best paths) Construction method CA polar Quantity of(J + J′) 19 bits (0b10100010101101111001, where a last bit is d19)

SNR values required when a BLER reaches 10⁻² and 10⁻³ are respectivelyevaluated. To be specific, sequences A and B are given. Each combination(N, K) is investigated based on the simulation parameter in theforegoing table. For example, N=64, and K=10. An SNR value required whenBLER=10⁻² by a polar code using the sequence A is denoted as HA, and anSNR value required when BLER=10⁻² by a polar code using the sequence Bis denoted as HB. An interpolation HA-HB of the SNR values is comparedwith a given threshold. If the interpolation HA-HB is greater than thethreshold, it is recorded that the sequence B wins, a win count of thesequence B is incremented by 1, and a fail count of the sequence A isincremented by 1. If the interpolation HA-HB is less than a negativethreshold, it is recorded that the sequence A wins, a win count of thesequence A is incremented by 1, and a fail count of the sequence B isincremented by 1. If the interpolation HA-HB is less than or equal tothe threshold or greater than or equal to the negative threshold, it isrecorded that the two sequences have same performance, and neither ofthe win counts of the two sequences is incremented. Further, SNR valuesrequired by the sequences A and B when BLER=10⁻³ is reached are furtherinvestigated, an interpolation is compared with a threshold, and anoperation is further performed on a win count.

Steps of determining the foregoing threshold are as follows.

When a length K of to-be-coded information is less than or equal to 200,PerfThresh_K=0.1 dB; or when K is greater than 200, PerfThresh_K=0.3 dB.

When a quantity of decoding lists is L=1, PerfThresh_L=0.4 dB; when L=2,PerfThresh_L=0.2 dB; or when L is another value, PerfThresh_L=0.1 dB.

A larger value in the two thresholds is selected as a final threshold,that is, PerfThresh=max (PerfThresh_K, PerfThresh_L).

A specific sequence comparison procedure is as follows.

Step 1: Calculate a win count, a fail count, and an overall fail countfor each sequence. The sequence A is selected, and the sequence A iscompared with the sequence B in each simulation case. For eachsimulation case, if performance of A is worse than that of B byPerfThresh, a fail count FailCount_AB of A versus B is incremented by 1;or if performance of A is better than that of B by PerfThresh, a wincount WinCountAB of A versus B is incremented by 1. If(FailCount_AB−WinCountAB)/a total quantity of simulation cases >2%, anoverall fail count OverallFail_A of A is incremented by 1. The sequenceA is compared with a sequence C in each simulation case. For eachsimulation case, if the performance of A is worse than that of C byPerfThresh, a fail count FailCount_AC of A versus C is incremented by 1;or if the performance of A is better than that of C by PerfThresh, aquantity of win times WinCount_AC of A versus C is incremented by 1. If(FailCount_AC−WinCountAC)/a total quantity of simulation cases >2%, theoverall fail count OverallFail_A of A is incremented by 1. The processis repeated for sequences D to N. The sequence B is selected, and thesequence B is compared with the sequence B in each simulation case, andso on. The sequence N is selected, and the sequence N is compared withthe sequence A, and so on. A sequence with a minimum overall fail countOverallFail is selected.

Step 2: If a plurality of sequences A to M each have a minimum overallfail count OverallFail, for the sequence A, the sequence A is comparedwith the sequence B in each simulation case. For each simulation case,if the performance of A is better than that of B by PerfThresh, the wincount WinCount_AB of A versus B is incremented by 1. The sequence A iscompared with the sequence C in each simulation case. For eachsimulation case, if the performance of A is better than that of C, byPerfThresh, the win count WinCount_AC of A versus C is incremented by 1,and an overall win count of A is WinCount A=ΣWinCount_AB . . . AM. Theprocess is repeated until the sequence A is compared with the sequenceM. The process is repeated for sequences B to M. A sequence with amaximum overall win count WinCount is selected, and it is assumed thatthe sequence is a sequence W.

Step 3: The sequence W with a maximum overall win count is given. Ifthere is a sequence x and a win count of x for W is greater than a wincount of W for x, namely WinCount_xW>WinCount Wx, the sequence x is alsoselected to enter a next round.

Step 4: If a plurality of sequences are selected, a final sequence isdetermined through voting.

It should be noted that the foregoing sequences S1 to S20 may be appliedin the polar coding method shown in FIG. 2 in this embodiment of thisapplication. In any sequence, adjustments or equivalent replacementsincluding but not limited to the following several aspects may be madewithout affecting an overall effect of the sequence.

1. Locations of a few elements in a sorting sequence are mutuallyexchanged. For example, a location of a sequence number may be adjustedwithin a specified amplitude. For example, the specified amplitude is 5,and a location of an element whose sequence number is 10 may be adjustedwithin a range from five locations on the left of the element to fivelocations on the right of the element.

2. Some elements in the sorting sequence are adjusted, but sets ofchannels that are used to transmit T-bit information and that areselected based on the sorting sequence may be the same or similar.

3. The sorting sequence includes N elements from 1 to N, and the Nelements from 1 to N represent sequence numbers of N polarized channels.Actually, the sequence numbers of the N polarized channels may beginwith 0 and end with N−1, and the sequence numbers may be obtained bysubtracting 1 from each sequence number in the sorting sequence. This isalso a form of a sequence number in the foregoing calculation manner.Certainly, another manner may alternatively be used to represent thesequence numbers or identifiers of the polarized channels, and thespecific expression manner does not affect specific locations of thepolarized channels represented in the sorting sequence.

4. The sequence numbers of the N polarized channels in the sortingsequence are arranged in descending order of reliability of the Npolarized channels. Actually, the sequence numbers of the N polarizedchannels may alternatively be arranged in ascending order of reliabilityof the N polarized channels. Elements in the sorting sequence arearranged in a reverse order.

5. The sorting sequence may further be represented by using a sortingsequence of normalized reliability or equivalent reliability of all thechannels. For example, if a sorting location of a channel x in thesequence is y (a minimum sequence number in the sorting sequence isdenoted as 1), reliability of the channel may be represented by y ornormalized y/N, where N is a length of the sorting sequence.

Based on the polar coding method shown in FIG. 2, as shown in FIG. 3, anembodiment of this application further provides a polar coding apparatus300. The polar coding apparatus 300 is configured to perform the polarcoding method shown in FIG. 2. The Polar coding apparatus 300 includes:

a determining unit 301, configured to determine a sequence used to codeto-be-coded bits, where the sequence is used to represent a reliabilityorder of N polarized channels, N is a mother code length of a polarcode, and N is a positive integer power of 2; and

a coding unit 302, configured to perform polar coding on the to-be-codedbits by using the sequence to obtain coded bits.

Optionally, a length of the to-be-coded bits is K, the K to-be-codedbits are mapped to K polarized channels in the N polarized channels, andreliability of the K polarized channels is higher than reliability ofremaining N−K polarized channels.

Optionally, the sequence may be a part or all of any one of thesequences (1) to (30) in the foregoing method, or may be a part or allof any one of the sequences S1 to S20 in the foregoing method.

Based on a same inventive concept as the polar coding method shown inFIG. 2, as shown in FIG. 4, an embodiment of this application furtherprovides a polar coding apparatus 400. The polar coding apparatus 400 isconfigured to perform the polar coding method shown in FIG. 2. A part orall of the polar coding method shown in FIG. 2 may be implemented byhardware or may be implemented by software. When the method isimplemented by using hardware, the polar coding apparatus 400 includes:an input interface circuit 401, configured to obtain to-be-coded bits; alogic circuit 402, configured to perform the polar coding method shownin FIG. 2, where reference may be made to the description in theforegoing method embodiment and details are not described herein again;and an output interface circuit 403, configured to output a coded bitsequence.

Optionally, in a specific implementation, the polar coding apparatus 400may be a chip or an integrated circuit.

Optionally, when a part or all of the polar coding method in theforegoing embodiment are implemented by using software, as shown in FIG.5, the polar coding apparatus 400 includes: a memory 501, configured tostore a program; and a processor 502, configured to execute the programstored in the memory 501. When the program is executed, the polar codingapparatus 400 may implement the polar coding method provided in theforegoing embodiment in FIG. 2.

Optionally, the memory 501 may be a physically independent unit, or asshown in FIG. 6, the memory 501 is integrated into the processor 502.

Optionally, when a part or all of the coding method in the foregoingembodiment in FIG. 2 are implemented by using software, the polar codetransmission apparatus 400 may include only the processor 502. Thememory 501 configured to store a program is located outside the polarcode transmission apparatus 400. The processor 502 is connected to thememory 501 by using a circuit/wire, and is configured to read andexecute the program stored in the memory 501.

The processor 502 may be a central processing unit (CPU), a networkprocessor (NP), or a combination of a CPU and an NP.

The processor 502 may further include a hardware chip. The hardware chipmay be an application-specific integrated circuit (ASIC), a programmablelogic device (PLD), or a combination thereof. The PLD may be a complexprogrammable logical device (CPLD), a field-programmable gate array(FPGA), generic array logic (GAL), or any combination thereof.

The memory 501 may include a volatile memory, such as a random accessmemory (RAM); the memory 501 may include a nonvolatile memory, such as aflash memory, a hard disk drive (HDD), or a solid-state drive (SSD); orthe memory 501 may include a combination of the foregoing types ofmemories.

An embodiment of this application further provides a computer storagemedium. The computer storage medium stores a computer program, and thecomputer program includes an instruction used to perform the polarcoding method shown in FIG. 2.

An embodiment of this application further provides a computer programproduct including an instruction. When the computer program product runson a computer, the computer performs the polar coding method shown inFIG. 2.

A person skilled in the art should understand that the embodiments ofthis application may be provided as a method, a system, or a computerprogram product. Therefore, this application may use a form ofhardware-only embodiments, software-only embodiments, or embodimentswith a combination of software and hardware. Moreover, this applicationmay use a form of a computer program product that is implemented on oneor more computer-usable storage media (including but not limited to adisk memory, a CD-ROM, an optical memory, and the like) that includecomputer usable program code.

This application is described with reference to the flowcharts and/orblock diagrams of the method, the device (system), and the computerprogram product according to the embodiments of this application. Itshould be understood that computer program instructions may be used toimplement each process and/or each block in the flowcharts and/or theblock diagrams and a combination of a process and/or a block in theflowcharts and/or the block diagrams. These computer programinstructions may be provided for a general-purpose computer, a dedicatedcomputer, an embedded processor, or a processor of any otherprogrammable data processing device to generate a machine, so that theinstructions executed by a computer or a processor of any otherprogrammable data processing device generate an apparatus forimplementing a specific function in one or more processes in theflowcharts and/or in one or more blocks in the block diagrams.

These computer program instructions may be stored in a computer readablememory that can instruct the computer or any other programmable dataprocessing device to work in a specific manner, so that the instructionsstored in the computer readable memory generate an artifact thatincludes an instruction apparatus. The instruction apparatus implementsa specific function in one or more processes in the flowcharts and/or inone or more blocks in the block diagrams.

These computer program instructions may be loaded onto a computer oranother programmable data processing device, so that a series ofoperations and steps are performed on the computer or the anotherprogrammable device, thereby generating computer-implemented processing.Therefore, the instructions executed on the computer or the anotherprogrammable device provide steps for implementing a specific functionin one or more processes in the flowcharts and/or in one or more blocksin the block diagrams.

Although some embodiments of this application have been described, aperson skilled in the art can make changes and modifications to theseembodiments once they learn the basic inventive concept. Therefore, thefollowing claims are intended to be construed as to cover the preferredembodiments and all changes and modifications falling within the scopeof this application.

Obviously, a person skilled in the art can make various modificationsand variations to the embodiments of this application without departingfrom the spirit and scope of the embodiments of the present invention.This application is intended to cover these modifications and variationsprovided that they fall within the scope of protection defined by thefollowing claims and their equivalent technologies.

What is claimed is:
 1. A polar coding method, the method comprising:obtaining to-be-coded bits; obtaining a first sequence with a length N,wherein the first sequence comprises sequence numbers from 1 to Ncorresponding to N polarized channels and is used to represent areliability order of the N polarized channels, wherein N is a positiveinteger power of 2, wherein the reliability order of the N polarizedchannels in the first sequence is same as the reliability order of the Npolarized channels in a second sequence; and performing polar coding onthe to-be-coded bits by using the first sequence to obtain coded bits;wherein the second sequence comprises sequence numbers from 1 to N_(max)corresponding to N_(max) polarized channels and is used to represent areliability order of the N_(max) polarized channels, wherein the N_(max)sequence numbers are arranged in ascending order of reliability of theN_(max) polarized channels in the second sequence, wherein N_(max)≥N,wherein N_(max)=1024, and wherein: a location of a polarized channelwhose sequence number is 1 in the second sequence is the 1^(st)location; and a location of a polarized channel whose sequence number is17 in the second sequence is the 6^(th) location; and a location of apolarized channel whose sequence number is 33 in the second sequence isthe 7^(th) location; and a location of a polarized channel whosesequence number is 35 in the second sequence is the 22^(nd) location;and a location of a polarized channel whose sequence number is 25 in thesecond sequence is the 23^(st) location; and a location of a polarizedchannel whose sequence number is 8 in the second sequence is the 25^(th)location; and a location of a polarized channel whose sequence number is67 in the second sequence is the 27^(th) location; and a location of apolarized channel whose sequence number is 12 in the second sequence isthe 29^(th) location; and a location of a polarized channel whosesequence number is 41 in the second sequence is the 30^(th) location;and a location of a polarized channel whose sequence number is 14 in thesecond sequence is the 34^(th) location; and a location of a polarizedchannel whose sequence number is 23 in the second sequence is the48^(th) location; and a location of a polarized channel whose sequencenumber is 42 in the second sequence is the 56^(th) location; and alocation of a polarized channel whose sequence number is 145 in thesecond sequence is the 57^(th) location; and a location of a polarizedchannel whose sequence number is 29 in the second sequence is the58^(th) location; and a location of a polarized channel whose sequencenumber is 70 in the second sequence is the 59^(th) location; and alocation of a polarized channel whose sequence number is 85 in thesecond sequence is the 92^(nd) location; and a location of a polarizedchannel whose sequence number is 44 in the second sequence is the97^(th) location; and a location of a polarized channel whose sequencenumber is 99 in the second sequence is the 98^(th) location; and alocation of a polarized channel whose sequence number is 147 in thesecond sequence is the 103^(rd) location; and a location of a polarizedchannel whose sequence number is 72 in the second sequence is the104^(th) location; and a location of a polarized channel whose sequencenumber is 266 in the second sequence is the 106^(th) location; and alocation of a polarized channel whose sequence number is 162 in thesecond sequence is the 107^(th) location; and a location of a polarizedchannel whose sequence number is 274 in the second sequence is the117^(th) location; and a location of a polarized channel whose sequencenumber is 78 in the second sequence is the 124^(th) location; and alocation of a polarized channel whose sequence number is 277 in thesecond sequence is the 140^(th) location; and a location of a polarizedchannel whose sequence number is 140 in the second sequence is the144^(th) location; and a location of a polarized channel whose sequencenumber is 87 in the second sequence is the 146^(th) location; and alocation of a polarized channel whose sequence number is 143 in thesecond sequence is the 158^(th) location; and a location of a polarizedchannel whose sequence number is 151 in the second sequence is the183^(rd) location; and a location of a polarized channel whose sequencenumber is 114 in the second sequence is the 192^(nd) location; and alocation of a polarized channel whose sequence number is 155 in thesecond sequence is the 193^(rd) location; and a location of a polarizedchannel whose sequence number is 80 in the second sequence is the194^(th) location; and a location of a polarized channel whose sequencenumber is 280 in the second sequence is the 297^(th) location; and alocation of a polarized channel whose sequence number is 395 in thesecond sequence is the 330^(th) location; and a location of a polarizedchannel whose sequence number is 328 in the second sequence is the359^(th) location; and a location of a polarized channel whose sequencenumber is 403 in the second sequence is the 362^(nd) location; and alocation of a polarized channel whose sequence number is 897 in thesecond sequence is the 375^(th) location; and a location of a polarizedchannel whose sequence number is 595 in the second sequence is the376^(th) location; and a location of a polarized channel whose sequencenumber is 650 in the second sequence is the 379^(th) location; and alocation of a polarized channel whose sequence number is 772 in thesecond sequence is the 380^(th) location; and a location of a polarizedchannel whose sequence number is 540 in the second sequence is the382^(nd) location; and a location of a polarized channel whose sequencenumber is 218 in the second sequence is the 389^(th) location; and alocation of a polarized channel whose sequence number is 610 in thesecond sequence is the 391^(st) location; and a location of a polarizedchannel whose sequence number is 597 in the second sequence is the392^(nd) location; and a location of a polarized channel whose sequencenumber is 552 in the second sequence is the 393^(rd) location; and alocation of a polarized channel whose sequence number is 651 in thesecond sequence is the 394^(th) location; and a location of a polarizedchannel whose sequence number is 542 in the second sequence is the399^(th) location; and a location of a polarized channel whose sequencenumber is 774 in the second sequence is the 400^(th) location; and alocation of a polarized channel whose sequence number is 611 in thesecond sequence is the 401^(st) location; and a location of a polarizedchannel whose sequence number is 658 in the second sequence is the402^(nd) location; and a location of a polarized channel whose sequencenumber is 601 in the second sequence is the 405^(th) location; and alocation of a polarized channel whose sequence number is 653 in thesecond sequence is the 409^(th) location; and a location of a polarizedchannel whose sequence number is 314 in the second sequence is the412^(th) location; and a location of a polarized channel whose sequencenumber is 543 in the second sequence is the 414^(th) location; and alocation of a polarized channel whose sequence number is 335 in thesecond sequence is the 415^(th) location; and a location of a polarizedchannel whose sequence number is 556 in the second sequence is the417^(th) location; and a location of a polarized channel whose sequencenumber is 775 in the second sequence is the 418^(th) location; and alocation of a polarized channel whose sequence number is 659 in thesecond sequence is the 421^(st) location; and a location of a polarizedchannel whose sequence number is 613 in the second sequence is the422^(nd) location; and a location of a polarized channel whose sequencenumber is 342 in the second sequence is the 423^(rd) location; and alocation of a polarized channel whose sequence number is 778 in thesecond sequence is the 424^(th) location; and a location of a polarizedchannel whose sequence number is 425 in the second sequence is the427^(th) location; and a location of a polarized channel whose sequencenumber is 674 in the second sequence is the 429^(th) location; and alocation of a polarized channel whose sequence number is 584 in thesecond sequence is the 430^(th) location; and a location of a polarizedchannel whose sequence number is 184 in the second sequence is the433^(rd) location; and a location of a polarized channel whose sequencenumber is 558 in the second sequence is the 436^(th) location; and alocation of a polarized channel whose sequence number is 661 in thesecond sequence is the 437^(th) location; and a location of a polarizedchannel whose sequence number is 617 in the second sequence is the438^(th) location; and a location of a polarized channel whose sequencenumber is 779 in the second sequence is the 442^(nd) location; and alocation of a polarized channel whose sequence number is 564 in thesecond sequence is the 443^(rd) location; and a location of a polarizedchannel whose sequence number is 398 in the second sequence is the446^(th) location; and a location of a polarized channel whose sequencenumber is 358 in the second sequence is the 453^(rd) location; and alocation of a polarized channel whose sequence number is 363 in thesecond sequence is the 488^(th) location; and a location of a polarizedchannel whose sequence number is 721 in the second sequence is the548^(th) location; and a location of a polarized channel whose sequencenumber is 708 in the second sequence is the 593^(rd) location; and alocation of a polarized channel whose sequence number is 482 in thesecond sequence is the 616^(th) location; and a location of a polarizedchannel whose sequence number is 414 in the second sequence is the618^(th) location; and a location of a polarized channel whose sequencenumber is 604 in the second sequence is the 619^(th) location; and alocation of a polarized channel whose sequence number is 633 in thesecond sequence is the 636^(th) location; and a location of a polarizedchannel whose sequence number is 836 in the second sequence is the645^(th) location; and a location of a polarized channel whose sequencenumber is 913 in the second sequence is the 658^(th) location; and alocation of a polarized channel whose sequence number is 381 in thesecond sequence is the 678^(th) location; and a location of a polarizedchannel whose sequence number is 352 in the second sequence is the687^(th) location; and a location of a polarized channel whose sequencenumber is 684 in the second sequence is the 697^(th) location; and alocation of a polarized channel whose sequence number is 368 in thesecond sequence is the 708^(th) location; and a location of a polarizedchannel whose sequence number is 845 in the second sequence is the712^(th) location; and a location of a polarized channel whose sequencenumber is 906 in the second sequence is the 728^(th) location; and alocation of a polarized channel whose sequence number is 745 in thesecond sequence is the 732^(nd) location; and a location of a polarizedchannel whose sequence number is 716 in the second sequence is the739^(th) location; and a location of a polarized channel whose sequencenumber is 812 in the second sequence is the 749^(th) location; and alocation of a polarized channel whose sequence number is 490 in thesecond sequence is the 754^(th) location; and a location of a polarizedchannel whose sequence number is 477 in the second sequence is the761^(st) location; and a location of a polarized channel whose sequencenumber is 869 in the second sequence is the 768^(th) location; and alocation of a polarized channel whose sequence number is 624 in thesecond sequence is the 774^(th) location; and a location of a polarizedchannel whose sequence number is 727 in the second sequence is the784^(th) location; and a location of a polarized channel whose sequencenumber is 962 in the second sequence is the 785^(th) location; and alocation of a polarized channel whose sequence number is 632 in thesecond sequence is the 788^(th) location; and a location of a polarizedchannel whose sequence number is 730 in the second sequence is the789^(th) location; and a location of a polarized channel whose sequencenumber is 701 in the second sequence is the 790^(th) location; and alocation of a polarized channel whose sequence number is 742 in thesecond sequence is the 792^(nd) location; and a location of a polarizedchannel whose sequence number is 846 in the second sequence is the793^(rd) location; and a location of a polarized channel whose sequencenumber is 921 in the second sequence is the 794^(th) location; and alocation of a polarized channel whose sequence number is 823 in thesecond sequence is the 796^(th) location; and a location of a polarizedchannel whose sequence number is 852 in the second sequence is the797^(th) location; and a location of a polarized channel whose sequencenumber is 731 in the second sequence is the 798^(th) location; and alocation of a polarized channel whose sequence number is 881 in thesecond sequence is the 800^(th) location; and a location of a polarizedchannel whose sequence number is 743 in the second sequence is the801^(st) location; and a location of a polarized channel whose sequencenumber is 746 in the second sequence is the 811^(th) location; and alocation of a polarized channel whose sequence number is 827 in thesecond sequence is the 812^(th) location; and a location of a polarizedchannel whose sequence number is 733 in the second sequence is the813^(th) location; and a location of a polarized channel whose sequencenumber is 447 in the second sequence is the 814^(th) location; and alocation of a polarized channel whose sequence number is 963 in thesecond sequence is the 815^(th) location; and a location of a polarizedchannel whose sequence number is 937 in the second sequence is the816^(th) location; and a location of a polarized channel whose sequencenumber is 476 in the second sequence is the 817^(th) location; and alocation of a polarized channel whose sequence number is 854 in thesecond sequence is the 818^(th) location; and a location of a polarizedchannel whose sequence number is 868 in the second sequence is the819^(th) location; and a location of a polarized channel whose sequencenumber is 638 in the second sequence is the 820^(th) location; and alocation of a polarized channel whose sequence number is 908 in thesecond sequence is the 821^(st) location; and a location of a polarizedchannel whose sequence number is 488 in the second sequence is the822^(nd) location; and a location of a polarized channel whose sequencenumber is 696 in the second sequence is the 823^(rd) location; and alocation of a polarized channel whose sequence number is 747 in thesecond sequence is the 824^(th) location; and a location of a polarizedchannel whose sequence number is 829 in the second sequence is the825^(th) location; and a location of a polarized channel whose sequencenumber is 754 in the second sequence is the 826^(th) location; and alocation of a polarized channel whose sequence number is 855 in thesecond sequence is the 827^(th) location; and a location of a polarizedchannel whose sequence number is 858 in the second sequence is the828^(th) location; and a location of a polarized channel whose sequencenumber is 749 in the second sequence is the 838^(th) location; and alocation of a polarized channel whose sequence number is 945 in thesecond sequence is the 839^(th) location; and a location of a polarizedchannel whose sequence number is 755 in the second sequence is the843^(rd) location; and a location of a polarized channel whose sequencenumber is 918 in the second sequence is the 852^(nd) location; and alocation of a polarized channel whose sequence number is 728 in thesecond sequence is the 853^(rd) location; and a location of a polarizedchannel whose sequence number is 919 in the second sequence is the865^(th) location; and a location of a polarized channel whose sequencenumber is 503 in the second sequence is the 866^(th) location; and alocation of a polarized channel whose sequence number is 934 in thesecond sequence is the 867^(th) location; and a location of a polarizedchannel whose sequence number is 744 in the second sequence is the868^(th) location; and a location of a polarized channel whose sequencenumber is 761 in the second sequence is the 869^(th) location; and alocation of a polarized channel whose sequence number is 882 in thesecond sequence is the 870^(th) location; and a location of a polarizedchannel whose sequence number is 495 in the second sequence is the871^(st) location; and a location of a polarized channel whose sequencenumber is 703 in the second sequence is the 872^(nd) location; and alocation of a polarized channel whose sequence number is 922 in thesecond sequence is the 873^(rd) location; and a location of a polarizedchannel whose sequence number is 848 in the second sequence is the876^(th) location; and a location of a polarized channel whose sequencenumber is 993 in the second sequence is the 877^(th) location; and alocation of a polarized channel whose sequence number is 448 in thesecond sequence is the 878^(th) location; and a location of a polarizedchannel whose sequence number is 734 in the second sequence is the879^(th) location; and a location of a polarized channel whose sequencenumber is 828 in the second sequence is the 880^(th) location; and alocation of a polarized channel whose sequence number is 856 in thesecond sequence is the 887^(th) location; and a location of a polarizedchannel whose sequence number is 925 in the second sequence is the888^(th) location; and a location of a polarized channel whose sequencenumber is 735 in the second sequence is the 889^(th) location; and alocation of a polarized channel whose sequence number is 830 in thesecond sequence is the 890^(th) location; and a location of a polarizedchannel whose sequence number is 966 in the second sequence is the891^(st) location; and a location of a polarized channel whose sequencenumber is 939 in the second sequence is the 892^(nd) location; and alocation of a polarized channel whose sequence number is 885 in thesecond sequence is the 893^(rd) location; and a location of a polarizedchannel whose sequence number is 507 in the second sequence is the894^(th) location; and a location of a polarized channel whose sequencenumber is 750 in the second sequence is the 895^(th) location; and alocation of a polarized channel whose sequence number is 946 in thesecond sequence is the 896^(th) location; and a location of a polarizedchannel whose sequence number is 756 in the second sequence is the898^(th) location; and a location of a polarized channel whose sequencenumber is 831 in the second sequence is the 901^(st) location; and alocation of a polarized channel whose sequence number is 862 in thesecond sequence is the 911^(th) location; and a location of a polarizedchannel whose sequence number is 920 in the second sequence is the914^(th) location; and a location of a polarized channel whose sequencenumber is 973 in the second sequence is the 921^(st) location; and alocation of a polarized channel whose sequence number is 878 in thesecond sequence is the 923^(rd) location; and a location of a polarizedchannel whose sequence number is 953 in the second sequence is the924^(th) location; and a location of a polarized channel whose sequencenumber is 891 in the second sequence is the 954^(th) location; and alocation of a polarized channel whose sequence number is 999 in thesecond sequence is the 983^(rd) location; and a location of a polarizedchannel whose sequence number is 989 in the second sequence is the986^(th) location; and a location of a polarized channel whose sequencenumber is 1000 in the second sequence is the 1002^(nd) location; and alocation of a polarized channel whose sequence number is 1024 in thesecond sequence is the 1024^(th) location.
 2. The method according toclaim 1, wherein a length of the to-be-coded bits is K, and wherein theK to-be-coded bits are mapped to K polarized channels in the N polarizedchannels.
 3. The method according to claim 2, wherein the K to-be-codedbits comprise a number of K_(CRC) check bits.
 4. The method according toclaim 2, wherein the K polarized channels are selected based onreliability.
 5. The method according to claim 1, further comprisingperforming rate matching on the coded bits.
 6. A polar coding apparatus,the apparatus comprising: at least one processor; and a memory, thememory storing a program executable by the at least one processor,wherein the program, when executed by the at least one processor, causesone or more operations to be performed, the one or more operationscomprising: obtaining to-be-obtained bits; obtaining a first sequencewith a length N, wherein the first sequence comprises sequence numbersfrom 1 to N corresponding to N polarized channels and is used torepresent a reliability order of the N polarized channels, wherein N isa positive integer power of 2, wherein the reliability order of the Npolarized channels in the first sequence is same as the reliabilityorder of the N polarized channels in a second sequence; and performingpolar coding on the to-be-coded bits by using the first sequence withthe length N to obtain coded bits; wherein the second sequence comprisessequence numbers from 1 to N_(max) corresponding to N_(max) polarizedchannels and is used to represent a reliability order of the N_(max)polarized channels, wherein the N_(max) sequence numbers are arranged inascending order of reliability of the N_(max) polarized channels in thesecond sequence, wherein N_(max)≥N, wherein N_(max)=1024, and wherein: alocation of a polarized channel whose sequence number is 1 in the secondsequence is the 1^(st) location; and a location of a polarized channelwhose sequence number is 17 in the second sequence is the 6^(th)location; and a location of a polarized channel whose sequence number is33 in the second sequence is the 7^(th) location; and a location of apolarized channel whose sequence number is 35 in the second sequence isthe 22^(nd) location; and a location of a polarized channel whosesequence number is 25 in the second sequence is the 23^(st) location;and a location of a polarized channel whose sequence number is 8 in thesecond sequence is the 25^(th) location; and a location of a polarizedchannel whose sequence number is 67 in the second sequence is the27^(th) location; and a location of a polarized channel whose sequencenumber is 12 in the second sequence is the 29^(th) location; and alocation of a polarized channel whose sequence number is 41 in thesecond sequence is the 30^(th) location; and a location of a polarizedchannel whose sequence number is 14 in the second sequence is the34^(th) location; and a location of a polarized channel whose sequencenumber is 23 in the second sequence is the 48^(th) location; and alocation of a polarized channel whose sequence number is 42 in thesecond sequence is the 56^(th) location; and a location of a polarizedchannel whose sequence number is 145 in the second sequence is the57^(th) location; and a location of a polarized channel whose sequencenumber is 29 in the second sequence is the 58^(th) location; and alocation of a polarized channel whose sequence number is 70 in thesecond sequence is the 59^(th) location; and a location of a polarizedchannel whose sequence number is 85 in the second sequence is the92^(nd) location; and a location of a polarized channel whose sequencenumber is 44 in the second sequence is the 97^(th) location; and alocation of a polarized channel whose sequence number is 99 in thesecond sequence is the 98^(th) location; and a location of a polarizedchannel whose sequence number is 147 in the second sequence is the103^(rd) location; and a location of a polarized channel whose sequencenumber is 72 in the second sequence is the 104^(th) location; and alocation of a polarized channel whose sequence number is 266 in thesecond sequence is the 106^(th) location; and a location of a polarizedchannel whose sequence number is 162 in the second sequence is the107^(th) location; and a location of a polarized channel whose sequencenumber is 274 in the second sequence is the 117^(th) location; and alocation of a polarized channel whose sequence number is 78 in thesecond sequence is the 124^(th) location; and a location of a polarizedchannel whose sequence number is 277 in the second sequence is the140^(th) location; and a location of a polarized channel whose sequencenumber is 140 in the second sequence is the 144^(th) location; and alocation of a polarized channel whose sequence number is 87 in thesecond sequence is the 146^(th) location; and a location of a polarizedchannel whose sequence number is 143 in the second sequence is the158^(th) location; and a location of a polarized channel whose sequencenumber is 151 in the second sequence is the 183^(rd) location; and alocation of a polarized channel whose sequence number is 114 in thesecond sequence is the 192^(nd) location; and a location of a polarizedchannel whose sequence number is 155 in the second sequence is the193^(rd) location; and a location of a polarized channel whose sequencenumber is 80 in the second sequence is the 194^(th) location; and alocation of a polarized channel whose sequence number is 280 in thesecond sequence is the 297^(th) location; and a location of a polarizedchannel whose sequence number is 395 in the second sequence is the330^(th) location; and a location of a polarized channel whose sequencenumber is 328 in the second sequence is the 359^(th) location; and alocation of a polarized channel whose sequence number is 403 in thesecond sequence is the 362^(nd) location; and a location of a polarizedchannel whose sequence number is 897 in the second sequence is the375^(th) location; and a location of a polarized channel whose sequencenumber is 595 in the second sequence is the 376^(th) location; and alocation of a polarized channel whose sequence number is 650 in thesecond sequence is the 379^(th) location; and a location of a polarizedchannel whose sequence number is 772 in the second sequence is the380^(th) location; and a location of a polarized channel whose sequencenumber is 540 in the second sequence is the 382^(nd) location; and alocation of a polarized channel whose sequence number is 218 in thesecond sequence is the 389^(th) location; and a location of a polarizedchannel whose sequence number is 610 in the second sequence is the391^(st) location; and a location of a polarized channel whose sequencenumber is 597 in the second sequence is the 392^(nd) location; and alocation of a polarized channel whose sequence number is 552 in thesecond sequence is the 393^(rd) location; and a location of a polarizedchannel whose sequence number is 651 in the second sequence is the394^(th) location; and a location of a polarized channel whose sequencenumber is 542 in the second sequence is the 399^(th) location; and alocation of a polarized channel whose sequence number is 774 in thesecond sequence is the 400^(th) location; and a location of a polarizedchannel whose sequence number is 611 in the second sequence is the401^(st) location; and a location of a polarized channel whose sequencenumber is 658 in the second sequence is the 402^(nd) location; and alocation of a polarized channel whose sequence number is 601 in thesecond sequence is the 405^(th) location; and a location of a polarizedchannel whose sequence number is 653 in the second sequence is the409^(th) location; and a location of a polarized channel whose sequencenumber is 314 in the second sequence is the 412^(th) location; and alocation of a polarized channel whose sequence number is 543 in thesecond sequence is the 414^(th) location; and a location of a polarizedchannel whose sequence number is 335 in the second sequence is the415^(th) location; and a location of a polarized channel whose sequencenumber is 556 in the second sequence is the 417^(th) location; and alocation of a polarized channel whose sequence number is 775 in thesecond sequence is the 418^(th) location; and a location of a polarizedchannel whose sequence number is 659 in the second sequence is the421^(st) location; and a location of a polarized channel whose sequencenumber is 613 in the second sequence is the 422^(nd) location; and alocation of a polarized channel whose sequence number is 342 in thesecond sequence is the 423^(rd) location; and a location of a polarizedchannel whose sequence number is 778 in the second sequence is the424^(th) location; and a location of a polarized channel whose sequencenumber is 425 in the second sequence is the 427^(th) location; and alocation of a polarized channel whose sequence number is 674 in thesecond sequence is the 429^(th) location; and a location of a polarizedchannel whose sequence number is 584 in the second sequence is the430^(th) location; and a location of a polarized channel whose sequencenumber is 184 in the second sequence is the 433^(rd) location; and alocation of a polarized channel whose sequence number is 558 in thesecond sequence is the 436^(th) location; and a location of a polarizedchannel whose sequence number is 661 in the second sequence is the437^(th) location; and a location of a polarized channel whose sequencenumber is 617 in the second sequence is the 438^(th) location; and alocation of a polarized channel whose sequence number is 779 in thesecond sequence is the 442^(nd) location; and a location of a polarizedchannel whose sequence number is 564 in the second sequence is the443^(rd) location; and a location of a polarized channel whose sequencenumber is 398 in the second sequence is the 446^(th) location; and alocation of a polarized channel whose sequence number is 358 in thesecond sequence is the 453^(rd) location; and a location of a polarizedchannel whose sequence number is 363 in the second sequence is the488^(th) location; and a location of a polarized channel whose sequencenumber is 721 in the second sequence is the 548^(th) location; and alocation of a polarized channel whose sequence number is 708 in thesecond sequence is the 593^(rd) location; and a location of a polarizedchannel whose sequence number is 482 in the second sequence is the616^(th) location; and a location of a polarized channel whose sequencenumber is 414 in the second sequence is the 618^(th) location; and alocation of a polarized channel whose sequence number is 604 in thesecond sequence is the 619^(th) location; and a location of a polarizedchannel whose sequence number is 633 in the second sequence is the636^(th) location; and a location of a polarized channel whose sequencenumber is 836 in the second sequence is the 645^(th) location; and alocation of a polarized channel whose sequence number is 913 in thesecond sequence is the 658^(th) location; and a location of a polarizedchannel whose sequence number is 381 in the second sequence is the678^(th) location; and a location of a polarized channel whose sequencenumber is 352 in the second sequence is the 687^(th) location; and alocation of a polarized channel whose sequence number is 684 in thesecond sequence is the 697^(th) location; and a location of a polarizedchannel whose sequence number is 368 in the second sequence is the708^(th) location; and a location of a polarized channel whose sequencenumber is 845 in the second sequence is the 712^(th) location; and alocation of a polarized channel whose sequence number is 906 in thesecond sequence is the 728^(th) location; and a location of a polarizedchannel whose sequence number is 745 in the second sequence is the732^(nd) location; and a location of a polarized channel whose sequencenumber is 716 in the second sequence is the 739^(th) location; and alocation of a polarized channel whose sequence number is 812 in thesecond sequence is the 749^(th) location; and a location of a polarizedchannel whose sequence number is 490 in the second sequence is the754^(th) location; and a location of a polarized channel whose sequencenumber is 477 in the second sequence is the 761^(st) location; and alocation of a polarized channel whose sequence number is 869 in thesecond sequence is the 768^(th) location; and a location of a polarizedchannel whose sequence number is 624 in the second sequence is the774^(th) location; and a location of a polarized channel whose sequencenumber is 727 in the second sequence is the 784^(th) location; and alocation of a polarized channel whose sequence number is 962 in thesecond sequence is the 785^(th) location; and a location of a polarizedchannel whose sequence number is 632 in the second sequence is the788^(th) location; and a location of a polarized channel whose sequencenumber is 730 in the second sequence is the 789^(th) location; and alocation of a polarized channel whose sequence number is 701 in thesecond sequence is the 790^(th) location; and a location of a polarizedchannel whose sequence number is 742 in the second sequence is the792^(nd) location; and a location of a polarized channel whose sequencenumber is 846 in the second sequence is the 793^(rd) location; and alocation of a polarized channel whose sequence number is 921 in thesecond sequence is the 794^(th) location; and a location of a polarizedchannel whose sequence number is 823 in the second sequence is the796^(th) location; and a location of a polarized channel whose sequencenumber is 852 in the second sequence is the 797^(th) location; and alocation of a polarized channel whose sequence number is 731 in thesecond sequence is the 798^(th) location; and a location of a polarizedchannel whose sequence number is 881 in the second sequence is the800^(th) location; and a location of a polarized channel whose sequencenumber is 743 in the second sequence is the 801^(st) location; and alocation of a polarized channel whose sequence number is 746 in thesecond sequence is the 811^(th) location; and a location of a polarizedchannel whose sequence number is 827 in the second sequence is the812^(th) location; and a location of a polarized channel whose sequencenumber is 733 in the second sequence is the 813^(th) location; and alocation of a polarized channel whose sequence number is 447 in thesecond sequence is the 814^(th) location; and a location of a polarizedchannel whose sequence number is 963 in the second sequence is the815^(th) location; and a location of a polarized channel whose sequencenumber is 937 in the second sequence is the 816^(th) location; and alocation of a polarized channel whose sequence number is 476 in thesecond sequence is the 817^(th) location; and a location of a polarizedchannel whose sequence number is 854 in the second sequence is the818^(th) location; and a location of a polarized channel whose sequencenumber is 868 in the second sequence is the 819^(th) location; and alocation of a polarized channel whose sequence number is 638 in thesecond sequence is the 820^(th) location; and a location of a polarizedchannel whose sequence number is 908 in the second sequence is the821^(st) location; and a location of a polarized channel whose sequencenumber is 488 in the second sequence is the 822^(nd) location; and alocation of a polarized channel whose sequence number is 696 in thesecond sequence is the 823^(rd) location; and a location of a polarizedchannel whose sequence number is 747 in the second sequence is the824^(th) location; and a location of a polarized channel whose sequencenumber is 829 in the second sequence is the 825^(th) location; and alocation of a polarized channel whose sequence number is 754 in thesecond sequence is the 826^(th) location; and a location of a polarizedchannel whose sequence number is 855 in the second sequence is the827^(th) location; and a location of a polarized channel whose sequencenumber is 858 in the second sequence is the 828^(th) location; and alocation of a polarized channel whose sequence number is 749 in thesecond sequence is the 838^(th) location; and a location of a polarizedchannel whose sequence number is 945 in the second sequence is the839^(th) location; and a location of a polarized channel whose sequencenumber is 755 in the second sequence is the 843^(rd) location; and alocation of a polarized channel whose sequence number is 918 in thesecond sequence is the 852^(nd) location; and a location of a polarizedchannel whose sequence number is 728 in the second sequence is the853^(rd) location; and a location of a polarized channel whose sequencenumber is 919 in the second sequence is the 865^(th) location; and alocation of a polarized channel whose sequence number is 503 in thesecond sequence is the 866^(th) location; and a location of a polarizedchannel whose sequence number is 934 in the second sequence is the867^(th) location; and a location of a polarized channel whose sequencenumber is 744 in the second sequence is the 868^(th) location; and alocation of a polarized channel whose sequence number is 761 in thesecond sequence is the 869^(th) location; and a location of a polarizedchannel whose sequence number is 882 in the second sequence is the870^(th) location; and a location of a polarized channel whose sequencenumber is 495 in the second sequence is the 871^(st) location; and alocation of a polarized channel whose sequence number is 703 in thesecond sequence is the 872^(nd) location; and a location of a polarizedchannel whose sequence number is 922 in the second sequence is the873^(rd) location; and a location of a polarized channel whose sequencenumber is 848 in the second sequence is the 876^(th) location; and alocation of a polarized channel whose sequence number is 993 in thesecond sequence is the 877^(th) location; and a location of a polarizedchannel whose sequence number is 448 in the second sequence is the878^(th) location; and a location of a polarized channel whose sequencenumber is 734 in the second sequence is the 879^(th) location; and alocation of a polarized channel whose sequence number is 828 in thesecond sequence is the 880^(th) location; and a location of a polarizedchannel whose sequence number is 856 in the second sequence is the887^(th) location; and a location of a polarized channel whose sequencenumber is 925 in the second sequence is the 888^(th) location; and alocation of a polarized channel whose sequence number is 735 in thesecond sequence is the 889^(th) location; and a location of a polarizedchannel whose sequence number is 830 in the second sequence is the890^(th) location; and a location of a polarized channel whose sequencenumber is 966 in the second sequence is the 891^(st) location; and alocation of a polarized channel whose sequence number is 939 in thesecond sequence is the 892^(nd) location; and a location of a polarizedchannel whose sequence number is 885 in the second sequence is the893^(rd) location; and a location of a polarized channel whose sequencenumber is 507 in the second sequence is the 894^(th) location; and alocation of a polarized channel whose sequence number is 750 in thesecond sequence is the 895^(th) location; and a location of a polarizedchannel whose sequence number is 946 in the second sequence is the896^(th) location; and a location of a polarized channel whose sequencenumber is 756 in the second sequence is the 898^(th) location; and alocation of a polarized channel whose sequence number is 831 in thesecond sequence is the 901^(st) location; and a location of a polarizedchannel whose sequence number is 862 in the second sequence is the911^(th) location; and a location of a polarized channel whose sequencenumber is 920 in the second sequence is the 914^(th) location; and alocation of a polarized channel whose sequence number is 973 in thesecond sequence is the 921^(st) location; and a location of a polarizedchannel whose sequence number is 878 in the second sequence is the923^(rd) location; and a location of a polarized channel whose sequencenumber is 953 in the second sequence is the 924^(th) location; and alocation of a polarized channel whose sequence number is 891 in thesecond sequence is the 954^(th) location; and a location of a polarizedchannel whose sequence number is 999 in the second sequence is the983^(rd) location; and a location of a polarized channel whose sequencenumber is 989 in the second sequence is the 986^(th) location; and alocation of a polarized channel whose sequence number is 1000 in thesecond sequence is the 1002^(nd) location; and a location of a polarizedchannel whose sequence number is 1024 in the second sequence is the1024^(th) location.
 7. The apparatus according to claim 6, wherein alength of the to-be-coded bits is K, and wherein the K to-be-coded bitsare mapped to K polarized channels in the N polarized channels.
 8. Theapparatus according to claim 7, wherein the K to-be-coded bits comprisea number of K_(CRC) check bits.
 9. The apparatus according to claim 7,wherein the K polarized channels are selected based on reliability. 10.The apparatus according to claim 6, wherein the one or more operationsfurther comprise performing rate matching on the coded bits.
 11. Theapparatus according to claim 6, wherein the apparatus is a chip or anintegrated circuit.
 12. A polar coding apparatus, the apparatuscomprising: an input interface circuit, the input interface circuitconfigured to obtain to-be-coded bits; a logic circuit, the logiccircuit configured to perform: obtaining a first sequence with a lengthN, wherein the first sequence comprises sequence numbers from 1 to Ncorresponding to N polarized channels and is used to represent areliability order of the N polarized channels, wherein N is a positiveinteger power of 2, wherein the reliability order of the N polarizedchannels in the first sequence is same as the reliability order of the Npolarized channels in a second sequence; and performing polar coding onthe to-be-coded bits by using the first sequence with the length N toobtain coded bits; and an output interface circuit, the output interfacecircuit configured to output the coded bits; wherein the second sequencecomprises sequence numbers from 1 to N_(max) corresponding to N_(max)polarized channels and is used to represent a reliability order of theN_(max) polarized channels, wherein the N_(max) sequence numbers arearranged in ascending order of reliability of the N_(max) polarizedchannels in the second sequence, wherein N_(max)≥N, whereinN_(max)=1024, and wherein: a location of a polarized channel whosesequence number is 1 in the second sequence is the 1^(st) location; anda location of a polarized channel whose sequence number is 17 in thesecond sequence is the 6^(th) location; and a location of a polarizedchannel whose sequence number is 33 in the second sequence is the 7^(th)location; and a location of a polarized channel whose sequence number is35 in the second sequence is the 22^(nd) location; and a location of apolarized channel whose sequence number is 25 in the second sequence isthe 23^(rd) location; and a location of a polarized channel whosesequence number is 8 in the second sequence is the 25^(th) location; anda location of a polarized channel whose sequence number is 67 in thesecond sequence is the 27^(th) location; and a location of a polarizedchannel whose sequence number is 12 in the second sequence is the29^(th) location; and a location of a polarized channel whose sequencenumber is 41 in the second sequence is the 30^(th) location; and alocation of a polarized channel whose sequence number is 14 in thesecond sequence is the 34^(th) location; and a location of a polarizedchannel whose sequence number is 23 in the second sequence is the48^(th) location; and a location of a polarized channel whose sequencenumber is 42 in the second sequence is the 56^(th) location; and alocation of a polarized channel whose sequence number is 145 in thesecond sequence is the 57^(th) location; and a location of a polarizedchannel whose sequence number is 29 in the second sequence is the58^(th) location; and a location of a polarized channel whose sequencenumber is 70 in the second sequence is the 59^(th) location; and alocation of a polarized channel whose sequence number is 85 in thesecond sequence is the 92^(nd) location; and a location of a polarizedchannel whose sequence number is 44 in the second sequence is the97^(th) location; and a location of a polarized channel whose sequencenumber is 99 in the second sequence is the 98^(th) location; and alocation of a polarized channel whose sequence number is 147 in thesecond sequence is the 103^(rd) location; and a location of a polarizedchannel whose sequence number is 72 in the second sequence is the104^(th) location; and a location of a polarized channel whose sequencenumber is 266 in the second sequence is the 106^(th) location; and alocation of a polarized channel whose sequence number is 162 in thesecond sequence is the 107^(th) location; and a location of a polarizedchannel whose sequence number is 274 in the second sequence is the117^(th) location; and a location of a polarized channel whose sequencenumber is 78 in the second sequence is the 124^(th) location; and alocation of a polarized channel whose sequence number is 277 in thesecond sequence is the 140^(th) location; and a location of a polarizedchannel whose sequence number is 140 in the second sequence is the144^(th) location; and a location of a polarized channel whose sequencenumber is 87 in the second sequence is the 146^(th) location; and alocation of a polarized channel whose sequence number is 143 in thesecond sequence is the 158^(th) location; and a location of a polarizedchannel whose sequence number is 151 in the second sequence is the183^(rd) location; and a location of a polarized channel whose sequencenumber is 114 in the second sequence is the 192^(nd) location; and alocation of a polarized channel whose sequence number is 155 in thesecond sequence is the 193^(rd) location; and a location of a polarizedchannel whose sequence number is 80 in the second sequence is the194^(th) location; and a location of a polarized channel whose sequencenumber is 280 in the second sequence is the 297^(th) location; and alocation of a polarized channel whose sequence number is 395 in thesecond sequence is the 330^(th) location; and a location of a polarizedchannel whose sequence number is 328 in the second sequence is the359^(th) location; and a location of a polarized channel whose sequencenumber is 403 in the second sequence is the 362^(nd) location; and alocation of a polarized channel whose sequence number is 897 in thesecond sequence is the 375^(th) location; and a location of a polarizedchannel whose sequence number is 595 in the second sequence is the376^(th) location; and a location of a polarized channel whose sequencenumber is 650 in the second sequence is the 379^(th) location; and alocation of a polarized channel whose sequence number is 772 in thesecond sequence is the 380^(th) location; and a location of a polarizedchannel whose sequence number is 540 in the second sequence is the382^(nd) location; and a location of a polarized channel whose sequencenumber is 218 in the second sequence is the 389^(th) location; and alocation of a polarized channel whose sequence number is 610 in thesecond sequence is the 391^(st) location; and a location of a polarizedchannel whose sequence number is 597 in the second sequence is the392^(nd) location; and a location of a polarized channel whose sequencenumber is 552 in the second sequence is the 393^(rd) location; and alocation of a polarized channel whose sequence number is 651 in thesecond sequence is the 394^(th) location; and a location of a polarizedchannel whose sequence number is 542 in the second sequence is the399^(th) location; and a location of a polarized channel whose sequencenumber is 774 in the second sequence is the 400^(th) location; and alocation of a polarized channel whose sequence number is 611 in thesecond sequence is the 401^(st) location; and a location of a polarizedchannel whose sequence number is 658 in the second sequence is the402^(nd) location; and a location of a polarized channel whose sequencenumber is 601 in the second sequence is the 405^(th) location; and alocation of a polarized channel whose sequence number is 653 in thesecond sequence is the 409^(th) location; and a location of a polarizedchannel whose sequence number is 314 in the second sequence is the412^(th) location; and a location of a polarized channel whose sequencenumber is 543 in the second sequence is the 414^(th) location; and alocation of a polarized channel whose sequence number is 335 in thesecond sequence is the 415^(th) location; and a location of a polarizedchannel whose sequence number is 556 in the second sequence is the417^(th) location; and a location of a polarized channel whose sequencenumber is 775 in the second sequence is the 418^(th) location; and alocation of a polarized channel whose sequence number is 659 in thesecond sequence is the 421^(st) location; and a location of a polarizedchannel whose sequence number is 613 in the second sequence is the422^(nd) location; and a location of a polarized channel whose sequencenumber is 342 in the second sequence is the 423^(rd) location; and alocation of a polarized channel whose sequence number is 778 in thesecond sequence is the 424^(th) location; and a location of a polarizedchannel whose sequence number is 425 in the second sequence is the427^(th) location; and a location of a polarized channel whose sequencenumber is 674 in the second sequence is the 429^(th) location; and alocation of a polarized channel whose sequence number is 584 in thesecond sequence is the 430^(th) location; and a location of a polarizedchannel whose sequence number is 184 in the second sequence is the433^(rd) location; and a location of a polarized channel whose sequencenumber is 558 in the second sequence is the 436^(th) location; and alocation of a polarized channel whose sequence number is 661 in thesecond sequence is the 437^(th) location; and a location of a polarizedchannel whose sequence number is 617 in the second sequence is the438^(th) location; and a location of a polarized channel whose sequencenumber is 779 in the second sequence is the 442^(nd) location; and alocation of a polarized channel whose sequence number is 564 in thesecond sequence is the 443^(rd) location; and a location of a polarizedchannel whose sequence number is 398 in the second sequence is the446^(th) location; and a location of a polarized channel whose sequencenumber is 358 in the second sequence is the 453^(rd) location; and alocation of a polarized channel whose sequence number is 363 in thesecond sequence is the 488^(th) location; and a location of a polarizedchannel whose sequence number is 721 in the second sequence is the548^(th) location; and a location of a polarized channel whose sequencenumber is 708 in the second sequence is the 593^(rd) location; and alocation of a polarized channel whose sequence number is 482 in thesecond sequence is the 616^(th) location; and a location of a polarizedchannel whose sequence number is 414 in the second sequence is the618^(th) location; and a location of a polarized channel whose sequencenumber is 604 in the second sequence is the 619^(th) location; and alocation of a polarized channel whose sequence number is 633 in thesecond sequence is the 636^(th) location; and a location of a polarizedchannel whose sequence number is 836 in the second sequence is the645^(th) location; and a location of a polarized channel whose sequencenumber is 913 in the second sequence is the 658^(th) location; and alocation of a polarized channel whose sequence number is 381 in thesecond sequence is the 678^(th) location; and a location of a polarizedchannel whose sequence number is 352 in the second sequence is the687^(th) location; and a location of a polarized channel whose sequencenumber is 684 in the second sequence is the 697^(th) location; and alocation of a polarized channel whose sequence number is 368 in thesecond sequence is the 708^(th) location; and a location of a polarizedchannel whose sequence number is 845 in the second sequence is the712^(th) location; and a location of a polarized channel whose sequencenumber is 906 in the second sequence is the 728^(th) location; and alocation of a polarized channel whose sequence number is 745 in thesecond sequence is the 732^(nd) location; and a location of a polarizedchannel whose sequence number is 716 in the second sequence is the739^(th) location; and a location of a polarized channel whose sequencenumber is 812 in the second sequence is the 749^(th) location; and alocation of a polarized channel whose sequence number is 490 in thesecond sequence is the 754^(th) location; and a location of a polarizedchannel whose sequence number is 477 in the second sequence is the761^(st) location; and a location of a polarized channel whose sequencenumber is 869 in the second sequence is the 768^(th) location; and alocation of a polarized channel whose sequence number is 624 in thesecond sequence is the 774^(th) location; and a location of a polarizedchannel whose sequence number is 727 in the second sequence is the784^(th) location; and a location of a polarized channel whose sequencenumber is 962 in the second sequence is the 785^(th) location; and alocation of a polarized channel whose sequence number is 632 in thesecond sequence is the 788^(th) location; and a location of a polarizedchannel whose sequence number is 730 in the second sequence is the789^(th) location; and a location of a polarized channel whose sequencenumber is 701 in the second sequence is the 790^(th) location; and alocation of a polarized channel whose sequence number is 742 in thesecond sequence is the 792^(nd) location; and a location of a polarizedchannel whose sequence number is 846 in the second sequence is the793^(rd) location; and a location of a polarized channel whose sequencenumber is 921 in the second sequence is the 794^(th) location; and alocation of a polarized channel whose sequence number is 823 in thesecond sequence is the 796^(th) location; and a location of a polarizedchannel whose sequence number is 852 in the second sequence is the797^(th) location; and a location of a polarized channel whose sequencenumber is 731 in the second sequence is the 798^(th) location; and alocation of a polarized channel whose sequence number is 881 in thesecond sequence is the 800^(th) location; and a location of a polarizedchannel whose sequence number is 743 in the second sequence is the801^(st) location; and a location of a polarized channel whose sequencenumber is 746 in the second sequence is the 811^(th) location; and alocation of a polarized channel whose sequence number is 827 in thesecond sequence is the 812^(th) location; and a location of a polarizedchannel whose sequence number is 733 in the second sequence is the813^(th) location; and a location of a polarized channel whose sequencenumber is 447 in the second sequence is the 814^(th) location; and alocation of a polarized channel whose sequence number is 963 in thesecond sequence is the 815^(th) location; and a location of a polarizedchannel whose sequence number is 937 in the second sequence is the816^(th) location; and a location of a polarized channel whose sequencenumber is 476 in the second sequence is the 817^(th) location; and alocation of a polarized channel whose sequence number is 854 in thesecond sequence is the 818^(th) location; and a location of a polarizedchannel whose sequence number is 868 in the second sequence is the819^(th) location; and a location of a polarized channel whose sequencenumber is 638 in the second sequence is the 820^(th) location; and alocation of a polarized channel whose sequence number is 908 in thesecond sequence is the 821^(st) location; and a location of a polarizedchannel whose sequence number is 488 in the second sequence is the822^(nd) location; and a location of a polarized channel whose sequencenumber is 696 in the second sequence is the 823^(rd) location; and alocation of a polarized channel whose sequence number is 747 in thesecond sequence is the 824^(th) location; and a location of a polarizedchannel whose sequence number is 829 in the second sequence is the825^(th) location; and a location of a polarized channel whose sequencenumber is 754 in the second sequence is the 826^(th) location; and alocation of a polarized channel whose sequence number is 855 in thesecond sequence is the 827^(th) location; and a location of a polarizedchannel whose sequence number is 858 in the second sequence is the828^(th) location; and a location of a polarized channel whose sequencenumber is 749 in the second sequence is the 838^(th) location; and alocation of a polarized channel whose sequence number is 945 in thesecond sequence is the 839^(th) location; and a location of a polarizedchannel whose sequence number is 755 in the second sequence is the843^(rd) location; and a location of a polarized channel whose sequencenumber is 918 in the second sequence is the 852^(nd) location; and alocation of a polarized channel whose sequence number is 728 in thesecond sequence is the 853^(rd) location; and a location of a polarizedchannel whose sequence number is 919 in the second sequence is the865^(th) location; and a location of a polarized channel whose sequencenumber is 503 in the second sequence is the 866^(th) location; and alocation of a polarized channel whose sequence number is 934 in thesecond sequence is the 867^(th) location; and a location of a polarizedchannel whose sequence number is 744 in the second sequence is the868^(th) location; and a location of a polarized channel whose sequencenumber is 761 in the second sequence is the 869^(th) location; and alocation of a polarized channel whose sequence number is 882 in thesecond sequence is the 870^(th) location; and a location of a polarizedchannel whose sequence number is 495 in the second sequence is the871^(st) location; and a location of a polarized channel whose sequencenumber is 703 in the second sequence is the 872^(nd) location; and alocation of a polarized channel whose sequence number is 922 in thesecond sequence is the 873^(rd) location; and a location of a polarizedchannel whose sequence number is 848 in the second sequence is the876^(th) location; and a location of a polarized channel whose sequencenumber is 993 in the second sequence is the 877^(th) location; and alocation of a polarized channel whose sequence number is 448 in thesecond sequence is the 878^(th) location; and a location of a polarizedchannel whose sequence number is 734 in the second sequence is the879^(th) location; and a location of a polarized channel whose sequencenumber is 828 in the second sequence is the 880^(th) location; and alocation of a polarized channel whose sequence number is 856 in thesecond sequence is the 887^(th) location; and a location of a polarizedchannel whose sequence number is 925 in the second sequence is the888^(th) location; and a location of a polarized channel whose sequencenumber is 735 in the second sequence is the 889^(th) location; and alocation of a polarized channel whose sequence number is 830 in thesecond sequence is the 890^(th) location; and a location of a polarizedchannel whose sequence number is 966 in the second sequence is the891^(st) location; and a location of a polarized channel whose sequencenumber is 939 in the second sequence is the 892^(nd) location; and alocation of a polarized channel whose sequence number is 885 in thesecond sequence is the 893^(rd) location; and a location of a polarizedchannel whose sequence number is 507 in the second sequence is the894^(th) location; and a location of a polarized channel whose sequencenumber is 750 in the second sequence is the 895^(th) location; and alocation of a polarized channel whose sequence number is 946 in thesecond sequence is the 896^(th) location; and a location of a polarizedchannel whose sequence number is 756 in the second sequence is the898^(th) location; and a location of a polarized channel whose sequencenumber is 831 in the second sequence is the 901^(st) location; and alocation of a polarized channel whose sequence number is 862 in thesecond sequence is the 911^(th) location; and a location of a polarizedchannel whose sequence number is 920 in the second sequence is the914^(th) location; and a location of a polarized channel whose sequencenumber is 973 in the second sequence is the 921^(st) location; and alocation of a polarized channel whose sequence number is 878 in thesecond sequence is the 923^(rd) location; and a location of a polarizedchannel whose sequence number is 953 in the second sequence is the924^(th) location; and a location of a polarized channel whose sequencenumber is 891 in the second sequence is the 954^(th) location; and alocation of a polarized channel whose sequence number is 999 in thesecond sequence is the 983^(rd) location; and a location of a polarizedchannel whose sequence number is 989 in the second sequence is the986^(th) location; and a location of a polarized channel whose sequencenumber is 1000 in the second sequence is the 1002^(nd) location; and alocation of a polarized channel whose sequence number is 1024 in thesecond sequence is the 1024^(th) location.
 13. The apparatus accordingto claim 12, wherein a length of the to-be-coded bits is K, and whereinthe K to-be-coded bits are mapped to K polarized channels in the Npolarized channels.
 14. The apparatus according to claim 13, wherein theK to-be-coded bits comprise a number of K_(CRC) check bits.
 15. Theapparatus according to claim 13, wherein the K polarized channels areselected based on reliability.
 16. A non-transitory computer-readablestorage medium, wherein the non-transitory computer-readable storagemedium stores a computer program, wherein the computer program comprisesinstructions used to perform a polar coding method, and wherein theinstructions comprise: an instruction for obtaining to-be-coded bits; aninstruction for obtaining a first sequence with a length N, wherein thefirst sequence comprises sequence numbers from 1 to N corresponding to Npolarized channels and is used to represent a reliability order of the Npolarized channels, wherein N is a positive integer power of 2, whereinthe reliability order of the N polarized channels in the first sequenceis same as the reliability order of the N polarized channels in a secondsequence; and an instruction for performing polar coding on theto-be-coded bits by using the first sequence with the length N to obtaincoded bits; wherein the second sequence comprises sequence numbers from1 to N_(max) corresponding to N_(max) polarized channels and is used torepresent a reliability order of the N_(max) polarized channels, whereinthe N_(max) sequence numbers are arranged in ascending order ofreliability of the N_(max) polarized channels in the second sequence,wherein N_(max)≥N, wherein N_(max)=1024, and wherein: a location of apolarized channel whose sequence number is 1 in the second sequence isthe 1^(st) location; and a location of a polarized channel whosesequence number is 17 in the second sequence is the 6^(th) location; anda location of a polarized channel whose sequence number is 33 in thesecond sequence is the 7^(th) location; and a location of a polarizedchannel whose sequence number is 35 in the second sequence is the22^(nd) location; and a location of a polarized channel whose sequencenumber is 25 in the second sequence is the 23^(st) location; and alocation of a polarized channel whose sequence number is 8 in the secondsequence is the 25^(th) location; and a location of a polarized channelwhose sequence number is 67 in the second sequence is the 27^(th)location; and a location of a polarized channel whose sequence number is12 in the second sequence is the 29^(th) location; and a location of apolarized channel whose sequence number is 41 in the second sequence isthe 30^(th) location; and a location of a polarized channel whosesequence number is 14 in the second sequence is the 34^(th) location;and a location of a polarized channel whose sequence number is 23 in thesecond sequence is the 48^(th) location; and a location of a polarizedchannel whose sequence number is 42 in the second sequence is the56^(th) location; and a location of a polarized channel whose sequencenumber is 145 in the second sequence is the 57^(th) location; and alocation of a polarized channel whose sequence number is 29 in thesecond sequence is the 58^(th) location; and a location of a polarizedchannel whose sequence number is 70 in the second sequence is the59^(th) location; and a location of a polarized channel whose sequencenumber is 85 in the second sequence is the 92^(nd) location; and alocation of a polarized channel whose sequence number is 44 in thesecond sequence is the 97^(th) location; and a location of a polarizedchannel whose sequence number is 99 in the second sequence is the98^(th) location; and a location of a polarized channel whose sequencenumber is 147 in the second sequence is the 103^(rd) location; and alocation of a polarized channel whose sequence number is 72 in thesecond sequence is the 104^(th) location; and a location of a polarizedchannel whose sequence number is 266 in the second sequence is the106^(th) location; and a location of a polarized channel whose sequencenumber is 162 in the second sequence is the 107^(th) location; and alocation of a polarized channel whose sequence number is 274 in thesecond sequence is the 117^(th) location; and a location of a polarizedchannel whose sequence number is 78 in the second sequence is the124^(th) location; and a location of a polarized channel whose sequencenumber is 277 in the second sequence is the 140^(th) location; and alocation of a polarized channel whose sequence number is 140 in thesecond sequence is the 144^(th) location; and a location of a polarizedchannel whose sequence number is 87 in the second sequence is the146^(th) location; and a location of a polarized channel whose sequencenumber is 143 in the second sequence is the 158^(th) location; and alocation of a polarized channel whose sequence number is 151 in thesecond sequence is the 183^(rd) location; and a location of a polarizedchannel whose sequence number is 114 in the second sequence is the192^(nd) location; and a location of a polarized channel whose sequencenumber is 155 in the second sequence is the 193^(rd) location; and alocation of a polarized channel whose sequence number is 80 in thesecond sequence is the 194^(th) location; and a location of a polarizedchannel whose sequence number is 280 in the second sequence is the297^(th) location; and a location of a polarized channel whose sequencenumber is 395 in the second sequence is the 330^(th) location; and alocation of a polarized channel whose sequence number is 328 in thesecond sequence is the 359^(th) location; and a location of a polarizedchannel whose sequence number is 403 in the second sequence is the362^(nd) location; and a location of a polarized channel whose sequencenumber is 897 in the second sequence is the 375^(th) location; and alocation of a polarized channel whose sequence number is 595 in thesecond sequence is the 376^(th) location; and a location of a polarizedchannel whose sequence number is 650 in the second sequence is the379^(th) location; and a location of a polarized channel whose sequencenumber is 772 in the second sequence is the 380^(th) location; and alocation of a polarized channel whose sequence number is 540 in thesecond sequence is the 382^(nd) location; and a location of a polarizedchannel whose sequence number is 218 in the second sequence is the389^(th) location; and a location of a polarized channel whose sequencenumber is 610 in the second sequence is the 391^(st) location; and alocation of a polarized channel whose sequence number is 597 in thesecond sequence is the 392^(nd) location; and a location of a polarizedchannel whose sequence number is 552 in the second sequence is the393^(rd) location; and a location of a polarized channel whose sequencenumber is 651 in the second sequence is the 394^(th) location; and alocation of a polarized channel whose sequence number is 542 in thesecond sequence is the 399^(th) location; and a location of a polarizedchannel whose sequence number is 774 in the second sequence is the400^(th) location; and a location of a polarized channel whose sequencenumber is 611 in the second sequence is the 401^(st) location; and alocation of a polarized channel whose sequence number is 658 in thesecond sequence is the 402^(nd) location; and a location of a polarizedchannel whose sequence number is 601 in the second sequence is the405^(th) location; and a location of a polarized channel whose sequencenumber is 653 in the second sequence is the 409^(th) location; and alocation of a polarized channel whose sequence number is 314 in thesecond sequence is the 412^(th) location; and a location of a polarizedchannel whose sequence number is 543 in the second sequence is the414^(th) location; and a location of a polarized channel whose sequencenumber is 335 in the second sequence is the 415^(th) location; and alocation of a polarized channel whose sequence number is 556 in thesecond sequence is the 417^(th) location; and a location of a polarizedchannel whose sequence number is 775 in the second sequence is the418^(th) location; and a location of a polarized channel whose sequencenumber is 659 in the second sequence is the 421^(st) location; and alocation of a polarized channel whose sequence number is 613 in thesecond sequence is the 422^(nd) location; and a location of a polarizedchannel whose sequence number is 342 in the second sequence is the423^(rd) location; and a location of a polarized channel whose sequencenumber is 778 in the second sequence is the 424^(th) location; and alocation of a polarized channel whose sequence number is 425 in thesecond sequence is the 427^(th) location; and a location of a polarizedchannel whose sequence number is 674 in the second sequence is the429^(th) location; and a location of a polarized channel whose sequencenumber is 584 in the second sequence is the 430^(th) location; and alocation of a polarized channel whose sequence number is 184 in thesecond sequence is the 433^(rd) location; and a location of a polarizedchannel whose sequence number is 558 in the second sequence is the436^(th) location; and a location of a polarized channel whose sequencenumber is 661 in the second sequence is the 437^(th) location; and alocation of a polarized channel whose sequence number is 617 in thesecond sequence is the 438^(th) location; and a location of a polarizedchannel whose sequence number is 779 in the second sequence is the442^(nd) location; and a location of a polarized channel whose sequencenumber is 564 in the second sequence is the 443^(rd) location; and alocation of a polarized channel whose sequence number is 398 in thesecond sequence is the 446^(th) location; and a location of a polarizedchannel whose sequence number is 358 in the second sequence is the453^(rd) location; and a location of a polarized channel whose sequencenumber is 363 in the second sequence is the 488^(th) location; and alocation of a polarized channel whose sequence number is 721 in thesecond sequence is the 548^(th) location; and a location of a polarizedchannel whose sequence number is 708 in the second sequence is the593^(rd) location; and a location of a polarized channel whose sequencenumber is 482 in the second sequence is the 616^(th) location; and alocation of a polarized channel whose sequence number is 414 in thesecond sequence is the 618^(th) location; and a location of a polarizedchannel whose sequence number is 604 in the second sequence is the619^(th) location; and a location of a polarized channel whose sequencenumber is 633 in the second sequence is the 636^(th) location; and alocation of a polarized channel whose sequence number is 836 in thesecond sequence is the 645^(th) location; and a location of a polarizedchannel whose sequence number is 913 in the second sequence is the658^(th) location; and a location of a polarized channel whose sequencenumber is 381 in the second sequence is the 678^(th) location; and alocation of a polarized channel whose sequence number is 352 in thesecond sequence is the 687^(th) location; and a location of a polarizedchannel whose sequence number is 684 in the second sequence is the697^(th) location; and a location of a polarized channel whose sequencenumber is 368 in the second sequence is the 708^(th) location; and alocation of a polarized channel whose sequence number is 845 in thesecond sequence is the 712^(th) location; and a location of a polarizedchannel whose sequence number is 906 in the second sequence is the728^(th) location; and a location of a polarized channel whose sequencenumber is 745 in the second sequence is the 732^(nd) location; and alocation of a polarized channel whose sequence number is 716 in thesecond sequence is the 739^(th) location; and a location of a polarizedchannel whose sequence number is 812 in the second sequence is the749^(th) location; and a location of a polarized channel whose sequencenumber is 490 in the second sequence is the 754^(th) location; and alocation of a polarized channel whose sequence number is 477 in thesecond sequence is the 761^(st) location; and a location of a polarizedchannel whose sequence number is 869 in the second sequence is the768^(th) location; and a location of a polarized channel whose sequencenumber is 624 in the second sequence is the 774^(th) location; and alocation of a polarized channel whose sequence number is 727 in thesecond sequence is the 784^(th) location; and a location of a polarizedchannel whose sequence number is 962 in the second sequence is the785^(th) location; and a location of a polarized channel whose sequencenumber is 632 in the second sequence is the 788^(th) location; and alocation of a polarized channel whose sequence number is 730 in thesecond sequence is the 789^(th) location; and a location of a polarizedchannel whose sequence number is 701 in the second sequence is the790^(th) location; and a location of a polarized channel whose sequencenumber is 742 in the second sequence is the 792^(nd) location; and alocation of a polarized channel whose sequence number is 846 in thesecond sequence is the 793^(rd) location; and a location of a polarizedchannel whose sequence number is 921 in the second sequence is the794^(th) location; and a location of a polarized channel whose sequencenumber is 823 in the second sequence is the 796^(th) location; and alocation of a polarized channel whose sequence number is 852 in thesecond sequence is the 797^(th) location; and a location of a polarizedchannel whose sequence number is 731 in the second sequence is the798^(th) location; and a location of a polarized channel whose sequencenumber is 881 in the second sequence is the 800^(th) location; and alocation of a polarized channel whose sequence number is 743 in thesecond sequence is the 801^(st) location; and a location of a polarizedchannel whose sequence number is 746 in the second sequence is the811^(th) location; and a location of a polarized channel whose sequencenumber is 827 in the second sequence is the 812^(th) location; and alocation of a polarized channel whose sequence number is 733 in thesecond sequence is the 813^(th) location; and a location of a polarizedchannel whose sequence number is 447 in the second sequence is the814^(th) location; and a location of a polarized channel whose sequencenumber is 963 in the second sequence is the 815^(th) location; and alocation of a polarized channel whose sequence number is 937 in thesecond sequence is the 816^(th) location; and a location of a polarizedchannel whose sequence number is 476 in the second sequence is the817^(th) location; and a location of a polarized channel whose sequencenumber is 854 in the second sequence is the 818^(th) location; and alocation of a polarized channel whose sequence number is 868 in thesecond sequence is the 819^(th) location; and a location of a polarizedchannel whose sequence number is 638 in the second sequence is the820^(th) location; and a location of a polarized channel whose sequencenumber is 908 in the second sequence is the 821^(st) location; and alocation of a polarized channel whose sequence number is 488 in thesecond sequence is the 822^(nd) location; and a location of a polarizedchannel whose sequence number is 696 in the second sequence is the823^(rd) location; and a location of a polarized channel whose sequencenumber is 747 in the second sequence is the 824^(th) location; and alocation of a polarized channel whose sequence number is 829 in thesecond sequence is the 825^(th) location; and a location of a polarizedchannel whose sequence number is 754 in the second sequence is the826^(th) location; and a location of a polarized channel whose sequencenumber is 855 in the second sequence is the 827^(th) location; and alocation of a polarized channel whose sequence number is 858 in thesecond sequence is the 828^(th) location; and a location of a polarizedchannel whose sequence number is 749 in the second sequence is the838^(th) location; and a location of a polarized channel whose sequencenumber is 945 in the second sequence is the 839^(th) location; and alocation of a polarized channel whose sequence number is 755 in thesecond sequence is the 843^(rd) location; and a location of a polarizedchannel whose sequence number is 918 in the second sequence is the852^(nd) location; and a location of a polarized channel whose sequencenumber is 728 in the second sequence is the 853^(rd) location; and alocation of a polarized channel whose sequence number is 919 in thesecond sequence is the 865^(th) location; and a location of a polarizedchannel whose sequence number is 503 in the second sequence is the866^(th) location; and a location of a polarized channel whose sequencenumber is 934 in the second sequence is the 867^(th) location; and alocation of a polarized channel whose sequence number is 744 in thesecond sequence is the 868^(th) location; and a location of a polarizedchannel whose sequence number is 761 in the second sequence is the869^(th) location; and a location of a polarized channel whose sequencenumber is 882 in the second sequence is the 870^(th) location; and alocation of a polarized channel whose sequence number is 495 in thesecond sequence is the 871^(st) location; and a location of a polarizedchannel whose sequence number is 703 in the second sequence is the872^(nd) location; and a location of a polarized channel whose sequencenumber is 922 in the second sequence is the 873^(rd) location; and alocation of a polarized channel whose sequence number is 848 in thesecond sequence is the 876^(th) location; and a location of a polarizedchannel whose sequence number is 993 in the second sequence is the877^(th) location; and a location of a polarized channel whose sequencenumber is 448 in the second sequence is the 878^(th) location; and alocation of a polarized channel whose sequence number is 734 in thesecond sequence is the 879^(th) location; and a location of a polarizedchannel whose sequence number is 828 in the second sequence is the880^(th) location; and a location of a polarized channel whose sequencenumber is 856 in the second sequence is the 887^(th) location; and alocation of a polarized channel whose sequence number is 925 in thesecond sequence is the 888^(th) location; and a location of a polarizedchannel whose sequence number is 735 in the second sequence is the889^(th) location; and a location of a polarized channel whose sequencenumber is 830 in the second sequence is the 890^(th) location; and alocation of a polarized channel whose sequence number is 966 in thesecond sequence is the 891^(st) location; and a location of a polarizedchannel whose sequence number is 939 in the second sequence is the892^(nd) location; and a location of a polarized channel whose sequencenumber is 885 in the second sequence is the 893^(rd) location; and alocation of a polarized channel whose sequence number is 507 in thesecond sequence is the 894^(th) location; and a location of a polarizedchannel whose sequence number is 750 in the second sequence is the895^(th) location; and a location of a polarized channel whose sequencenumber is 946 in the second sequence is the 896^(th) location; and alocation of a polarized channel whose sequence number is 756 in thesecond sequence is the 898^(th) location; and a location of a polarizedchannel whose sequence number is 831 in the second sequence is the901^(st) location; and a location of a polarized channel whose sequencenumber is 862 in the second sequence is the 911^(th) location; and alocation of a polarized channel whose sequence number is 920 in thesecond sequence is the 914^(th) location; and a location of a polarizedchannel whose sequence number is 973 in the second sequence is the921^(st) location; and a location of a polarized channel whose sequencenumber is 878 in the second sequence is the 923^(rd) location; and alocation of a polarized channel whose sequence number is 953 in thesecond sequence is the 924^(th) location; and a location of a polarizedchannel whose sequence number is 891 in the second sequence is the954^(th) location; and a location of a polarized channel whose sequencenumber is 999 in the second sequence is the 983^(rd) location; and alocation of a polarized channel whose sequence number is 989 in thesecond sequence is the 986^(th) location; and a location of a polarizedchannel whose sequence number is 1000 in the second sequence is the1002^(nd) location; and a location of a polarized channel whose sequencenumber is 1024 in the second sequence is the 1024^(th) location.
 17. Thenon-transitory computer-readable storage medium according to claim 16,wherein a length of the to-be-coded bits is K, and wherein the Kto-be-coded bits are mapped to K polarized channels in the N polarizedchannels.
 18. The non-transitory computer-readable storage mediumaccording to claim 17, wherein the K to-be-coded bits comprise a numberof K_(CRC) check bits.
 19. The non-transitory computer-readable storagemedium according to claim 17, wherein the K polarized channels areselected based on reliability.
 20. The non-transitory computer-readablestorage medium according to claim 16, wherein the instructions furthercomprise an instruction for performing rate matching on the coded bits.